math reflection essay grade 10

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Reflecting on My Own Math Experiences

Hi thank you so much for being here..

Welcome! I am so glad you have come across this post! My name is Julia Park and I am a senior at Millersville University! I am an Early Childhood Education major and I have learned so much so far! If you have a moment, feel free to check out my previous blog posts!

In my last post, I shared information about learning centers in math class! In this post, I will be reflecting on my mathematical journey. My experiences in math have really shaped the way I teach my students.

My Early Math Memories

I believe that early math experiences can really shape a child’s mindset towards mathematics. It has definitely shaped mine. Unfortunately, it has been a long journey of growing my interest in math, and I am still working on it! 

When I was in elementary school, even up until my time at Millersville, math has been a huge struggle for me. I have grown up with the incredibly damaging misconception that you have to be a “math person” to excel in math.  A lot of my peers had the same mindset, which made it even harder to let go of those limiting thoughts. 

I discussed this in my growth mindset blog post , but “math people” do not exist! I have my own reasons as to why I thought there were math people, but children’s experiences often vary. I think my fixed mindset was formed from experiences with not-so-nice teachers, the pressure of time limits and the need for accuracy in class, and a lack of hands-on learning. Those are just a few ideas of why I think I have had a tough time with math and I will be discussing more ideas later in this post!

Although it was hard to get through math class sometimes, I am really grateful that I have had these experiences because I can learn from them and relate to my own students. I want my students to feel comfortable with asking for help and to know that it is possible to learn and grow in many ways!

What I Have Learned From Past Teachers

Through my time as a student in math class, I have had many different experiences with a variety of teachers. I want to share the good and the bad of what I have gone through because I think it is beneficial for teachers to reflect on all experiences related to learning. We can take what we learn to inform our own teaching practices. 

Positive approaches I have learned from teachers:

• Providing assistance outside of class
• Using a hands-on learning approach
• Giving time to practice skills in class
• Utilizing interactive math games
• Facilitating class discussions 
• Being kind and encouraging when a student is struggling 

Approaches of teachers that were difficult for me: 

• Focusing on accuracy only and not effort
• Putting pressure on students to turn in extensive assignments with a limited amount of time
• Teaching new concepts too fast
• Using too many lectures and PowerPoint presentations
• Not having time to reflect on concepts in class
• Being intimidating when a student is struggling 

Every student learns differently. These experiences are unique to me and not everyone will be able to relate to what I have taken from my past math classes. However, I think it is important to recognize that although one strategy might work for one student, it might not work for another student.  This notion emphasizes the need for differentiation. I will be discussing differentiation more in the next section. 

Strategies I Want to Use to Teach Math

As I finish this semester at Millersville University, I am leaving with so many new ways of teaching math that I was not even aware of previously. I have a new passion for making math class fun and interesting for my students. The following are some examples of strategies I would love to incorporate in my future math class: 

• My math instruction will be differentiated based on my students’ needs. I will monitor their progress through various assessments and observations to modify or individualize my instruction when needed.
• Hands-on learning will be included to increase the engagement and participation of my students. I want to make math fun and exciting!!
• Class discussions will be a huge part of my mathematics instruction. Discussions in math class promote a deeper understanding of mathematical concepts in children.  
• I would love to try to use interactive notebooks to organize my students’ learning and create engaging experiences. I had not heard of these notebooks until this year and I love them!
• Technology , manipulatives , and children’s literature are just a few tools I plan on using to enhance mathematics instruction for my students. 
• Parent involvement is very important for a child’s education and I will consistently keep in contact with families to increase this involvement. 
• I am very passionate about modeling a growth mindset for my students. I want my students to believe in themselves and in their ability to grow.
• I will strive to create a safe and welcoming environment for my students. I want them to be comfortable with sharing their ideas and to not fear making mistakes. To do this, I will value effort just as much as accuracy. 

Mistakes Are Learning Opportunities!

One of the biggest lessons I have learned throughout my time at Millersville is that making mistakes is okay. I used to put so much pressure on myself to be perfect and know everything, but that is not healthy. Teachers are not robots made to feed information to students. Instead, we have a purpose to learn alongside our students and to welcome mistakes as learning opportunities.

I am much more comfortable now being honest with my students in moments of uncertainty. I would rather figure something out with them than provide them with the wrong information. It’s really fun to explore ideas with students and work together toward a common goal. These experiences with students are valuable and strengthen the student-teacher relationship. When children trust their teachers, they are more engaged, motivated, and feel an increased amount of comfort when reaching out for help and sharing their thoughts with others. 

Check out my blog post about growth mindset to learn more about the importance of making mistakes and the value of having a positive mindset in math class!

Thank you so much for reading!

I had a blast sharing my mathematical experiences with you all! I have grown so much through the years and I can’t wait to keep growing as I gain more experience. I hope you learned about some ways you can teach mathematics in your own classroom! Thank you for reading. I sincerely appreciate it!

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Hi! I am Julia Park and I'm a junior at Millersville University. I am currently studying Early Childhood Education. I am so excited to share my journey through my new blog! View all posts by Julia Park

2 Ways to Encourage Reflection on Math Concepts

Open-ended questions guide students to participate and to think mathematically, which cements their learning.

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For many students, math is a subject where every question has one (and only one) correct answer. If a student is asked, “What is two plus two?” the only acceptable response is “Four.”

What if students were also asked, “Why does two plus two equal four?” Reflection questions like this, which are purposely open-ended, do not have a single correct answer. Instead, these questions remove the fear of being wrong and encourage mathematical thinking, participation, and growth.

“Reflection questions are important for students and help move the focus from performance to learning,” says Stanford professor Jo Boaler , who believes that “assessment plays a key role in the messages given to students about their potential, and many classrooms need to realign their assessment approach in order to encourage growth instead of fixed mindsets among students.”

In addition to performance-focused questions and assessments (“What is the total sum of the interior angles of a triangle?”), you can ask open-ended reflection questions that encourage mathematical thinking and participation (“Why do you think the total sum of the interior angles of a triangle always equals 180 degrees?”). The second question shifts the focus from performance toward thinking, learning, and engaging with mathematics without the fear of being wrong.

How can you incorporate reflection questions into your math lessons? Try these two useful strategies.

Which One Doesn’t Belong?

If you grew up watching Sesame Street , you probably remember the “One of These Things Is Not Like the Others” segment, where viewers had to identify one object out of a set of four that did not belong. This simple activity helps children to identify similarities and differences, and this type of thinking can be extended to learning math.

Which One Doesn’t Belong? (WODB) math activities present students with four different visual graphics that are all similar and different from each other in some way. This four-quadrant activity is my go-to for getting whole-class participation, as each option can be argued as the correct answer.

Observe the photo above of a WODB activity showing the numbers 22, 33, 44, and 50, and identify which choice does not belong and explain why. Since the graphics are purposely ambiguous and have overlapping similarities and differences, there is no single correct answer. One student might conclude that 50 doesn’t belong because it is the only number not divisible by 11. Another student may also believe that 50 doesn’t belong but for a different reason, namely that it is the only number with two different digits. A third student might conclude that 33 doesn’t belong because it is the only odd number. With this one graphic, you can easily spark a deep mathematical discussion where all students are eager to participate and share their thinking without any fear of being wrong.

WODB activities can be used for any math topic and can include images, numbers, charts, and graphs. They can also be used as formative assessments where students write their responses on sticky notes and stick them on the graphic that is projected at the front of the classroom.

Think-Notice-Wonder

Writing about math helps students organize their thoughts, use important vocabulary terms, and express their ideas in depth—which leads to deeper understanding.

Think-Notice-Wonder (TNW) activities are open-ended writing prompts where students are required to complete I think… , I notice… , I wonder… , based on a given graphic related to a math topic.

For example, students observe the soda and popcorn price graphic above and are prompted: What do you think? What do you notice? What do you wonder?

Encourage your students to think deeply for a minute or two before putting their thoughts into writing. They can share their ideas about the relationship between the price of a bag of popcorn and a soda based on size. They can verbalize how they perceive the proportional relationship to behave, wonder about which option provides the most value, and question how the prices were determined in the first place.

Since TNW writing activities are open-ended and do not have a correct answer, they encourage full group participation. Teachers often have students share their responses in a math journal notebook, but you can also use this free TNW student response template .

If you are looking for free images and graphics to use as TNW writing prompts, here are a few helpful resources:

• Find math-related graphics and images using Google Image Search and display them at the front of your classroom.
• Access and share teacher-created TNW activities on Twitter by searching the math education hashtags, including #ITeachMath, #MTBoS, and #NoticeWonder.
• Free stock photo websites such as Unsplash have an excellent collection of photos that relate to math topics, including estimation, three-dimensional figures, and mathematical patterns in nature.

When you add more reflection questions into your math lessons, students will have more opportunities to participate and engage in mathematical thinking without fear, which leads to a most-desired outcome—accessibility and growth.

Reflections Practice Questions

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Consortium to Promote Reflection in Engineering Education

Campus: green river college, 9. math test reflection essay.

Educator:  Mike Kenyon, Faculty, Mathematics Context:  Out of class; MATH 141 Pre-Calculus Keywords:  mathematics, essays Student Activity Time:  30 minutes

After completing an exam, students wrote a reflection essay about how the test went.

Introducing the Reflection Activity

One way to prompt students to think about their test performance is to simply ask for their first response to the test and their score. An educator used post-exam essays to prompt students to reflect on and articulate their reactions about the exam and their score. The purpose of this activity is to assist students in verbalizing their concerns, thoughts, and reactions to their graded exam.

The educator administered the regularly scheduled math exam, graded it, and returned the test to students with a solution key. The educator offered students a chance to earn a small portion of their homework grade by completing an essay about how the exam went and their reactions to it. The educator required students to write at least one double-spaced, typed page for their essay. Students often turned in reworked problems with the essay. The educator then graded the student’s submission and included a short 2-3 sentence response to their essay. The response generally included validation, answers to open questions, or recommendations that would assist the student in the future.

The educator used the information shared in the students’ essays in individual interactions with them, either in class or during office hours. When multiple students expressed similar concerns, the educator chose to respond to those concerns in class. As a result, students experienced an opportunity to articulate their successes, misconceptions and errors on the exam. Students often take action based on the educator’s response and suggestions, such as visiting office hours or the tutoring center to improve future exam performance.

 Recreating the Reflection Activity

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Math Essay | Essay on Math for Students and Children in English

February 13, 2024 by Prasanna

Math Essay: Mathematics is generally defined as the science that deals with numbers. It involves operations among numbers, and it also helps you to calculate the product price, how many discounted prizes here, and If you good in maths so you can calculate very fast. Mathematicians and scientists rely on mathematics principles in their real-life to experiments with new things every day. Many students say that ” I hate mathematics ” and maths is a useless subject, but it is wrong because without mathematics your life is tough to survive. Math has its applications in every field.

You can also find more  Essay Writing  articles on events, persons, sports, technology and many more.

Long and Short Essays on Math for Students and Kids in English

We are presenting students with essay samples on an extended essay of 500 words and a short of 150 words on the topic of math for reference.

Long Essay on Math 500 Words in English

Long Essay on Math is usually given to classes 7, 8, 9, and 10.

Mathematics is one of the common subjects that we study since our childhood. It is generally used in our daily life. Every person needs to learn some basics of it. Even counting money also includes math. Every work is linked with math in some way or the other. A person who does math is called a Mathematician.

Mathematics can be divided into two parts. The first is Pure mathematics, and the second is Applied mathematics. In Pure mathematics, we need to study the basic concept and structures of mathematics. But, on the other side, Applied mathematics involves the application of mathematics to solve problems that arise in various areas,(e.g.), science, engineering, and so on.

One couldn’t imagine the world without math. Math makes our life systematic, and every invention involves math. No matter what action a person is doing, he should know some basic maths. Every profession involves maths. Our present-day world runs on computers, and even computer runs with the help of maths. Every development that happens requires math.

Mathematics has a wide range of applications in our daily life. Maths generally deals with numbers. There are various topics in math, such as trigonometry; integration; differentiation, etc. All the subjects such as physics; chemistry; economy; commerce involve maths in some way or the other. Math is also used to find the relation between two numbers, and math is considered to be one of the most challenging subjects to learn. Math includes various numbers, and many symbols are used to show the relation between two different numbers.

Math is complicated to learn, and one needs to focus and concentrate more. Math is logical sometimes, and the logic needs to be derived out. Maths make our life easier and more straightforward. Math is considered to be challenging because it consists of many formulas that have to be learned, and many symbols and each symbol generally has its significance.

Some of the advantages of Math in our daily life

• Managing Money: Counting money and calculating simple interest, compound interest includes the usage of mathematics. Profit and loss are also computed using maths. Anything related to maths contains maths.
• Cooking: Maths is even used in cooking as estimating the number of ingredients that have to be used is calculated in numbers. Proportions also include maths.
• Home modelling: Calculating the area is essential in the construction of the home or home modelling. The size is also measured using maths. Even heights are also measured using maths.
• Travelling: Distance between two places and time taken to travel also includes maths. The amount of time taken revolves around maths. Almost every work is related to maths in some way or another. Maths contains some conditions that need to be followed, and maths has several formulas that have to be learned to become a mathematician.

Short Essay on Math 150 Words in English

Short Essay on Math is usually given to classes 1, 2, 3, 4, 5, and 6.

Maths is generally defined as the science of numbers and the operations performed among them. It deals with both alphabets along with numbers and involves addition, subtraction, multiplication, division, comparison, etc. It is used in every field. Maths consists of finding a relation between numbers, calculating the distance between two places, counting money, calculating profit and loss.

It is of two types pure and applied. Pure math deals with the basic structure and concept of maths, whereas applied mathematics deals with how maths is used it involves the application of maths in our daily life. All the subjects include maths, and hence maths is considered to be one of the primary and joint issues which need to be learned by everyone. One couldn’t imagine their life using maths. It has made our experience easy and straightforward. It has prevented chaos in our daily life. Hence learning maths is mandatory for everyone.

10 Lines on Math in English

• Father of Mathematics was Archimedes.
• Hypatia is the first woman know to know to have taught mathematics.
• From 0-1000 ,letter “A” only appears first in 1,000 ( “one thousand “).
• Zero (0) is the only number that can not be represented by Roman numerals.
• The Sign plus (+) and Minus(-) were discovered in 1489 A.D.
• Do you know that a Baseball field is of the perfect shape of a Rhombus.
• Jiffy is considered to be a unit of time for 1/100th of a second.
• 14th March International Day of Mathematics.
• Most mathematics symbols weren’t invented until the 16th century.
• The symbols for the division is called an Obelus.

FAQ’s on Math Essay

Question 1. What is Mathematics in simple words?

Answer: Mathematics is the study of shapes, patterns, numbers, and more. It involves a comparison between two numbers and calculating the distance between two places.

Question 2. Do we need mathematics every day?

Answer: Yes, we need mathematics every day, from buying a product to sell anything you want. Maths is present in our daily life, and no matter what work we do, maths is involved, and the application of maths is current in our everyday life.

Question 3. Who was the No.1 Mathematicians in the world?

Answer: Isaac Newton, who was a profound mathematician, is considered to be one of the best mathematicians in the world.

Question 4. What are the applications of maths?

Answer: Maths have various applications in our daily life. Maths is present everywhere from counting money to the calculating distance between two places. We could find math applications around.

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STANMORE SECONDARY

Exam Papers and Study Notes for grade 10 ,11 and 12

Maths(Grade 10)

Study notes, past year exam papers.

(updated 2024/06/15)

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Investigation March  QP & Memo

KZN  March  QP and Memo

FS  TEST 2 QP and Memo

FS TEST  QP and Memo

NW   Pre JUNE  QP only

KZN  June P1 and Memo

KZN  June P2 and Memo

FS   June  P1 and Memo

KZN  SEPT QP and Memo

LP March  QP and Memo

KZN  June  P1 and Memo

KZN June P2 and Memo

GP  June  P1 and Memo

GP  June  P2 and Memo

KZN  SEPT  QP and Memo

 NOV P1 and Memo

NOV  P2 and Memo

T 1 Investigation 2021 only

KZN March  QP and Memo  

FS  March  QP and Memo

LP  June   P1 and Memo

KZN June  QP and Memo 

KZN SEPT  QP and Memo  

NOV  P1 and Memo

April QP and Memo  

Local  April  QP only

June  QP and Memo

March QP + Memo

MARCH   QP and Memo

 June P1  and  Memo

June  P2  and  Memo

SEPT  QP  and Memo

NOV P1 and Memo

Nov-P2 and Memo

MARCH   QP and  MEMO

JUNE   QP  and  MEMO

SEPT  QP and  MEMO

NOV  P1  and MEMO

NOV P2   only

NOV P2  Answer Book

 Nov P2   Memo

MARCH  QP + MEMO

JUNE  QP  +  MEMO

SEPT  QP + MEMO

 NOV  P1  + MEMO

NOV P2   + MEMO

MARCH  QP+MEMO

DEPT – MARCH  QP+ MEMO

JUNE   QP+ MEMO

SEPT  QP+MEMO

NOV  P1 + MEMO

NOV  P2 + MEMO

JUNE   QP + MEMO

SEPT   QP + MEMO

NOV  P1    +  MEMO

 NOV P2    +  MEMO

Thursday, March 21, 2024

"growth and reflection: my journey in grade 10's third quarter".

The third quarter of Grade 10 has been a period of growth and self-reflection for me. As I look back on the past few months, I am filled with a sense of accomplishment and gratitude for the lessons I have learned and the progress I have made.

One of the key areas of growth for me during this quarter has been in my academic pursuits. I have challenged myself to take on more advanced subjects and push the boundaries of my knowledge. This has not been without its challenges, as I have encountered difficult concepts and demanding assignments. However, through perseverance and dedication, I have been able to overcome these obstacles and achieve success. The feeling of accomplishment that comes from mastering a difficult topic or receiving a good grade on a challenging assignment is truly rewarding and motivates me to continue striving for excellence.

In addition to academic growth, the third quarter has also been a time of self-reflection and personal development. I have taken the opportunity to reflect on my strengths and weaknesses, identifying areas for improvement and setting goals for myself. This process of self-reflection has allowed me to gain a deeper understanding of who I am as a person and what I want to achieve in the future. It has also helped me to develop important life skills such as time management, organization, and effective communication. I have learned that self-reflection is a powerful tool for personal growth and I plan to continue incorporating it into my life moving forward.

Overall, the third quarter of Grade 10 has been a transformative period for me. I have grown academically, developing a deeper understanding of various subjects, and I have also grown personally, gaining insights into my own strengths and areas for improvement. As I move forward into the next quarter and beyond, I am excited to continue building upon the foundation I have laid and continue my journey of growth and self-discovery.

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• ICSE Class 10
• ICSE Class 10 Selina Solutions
• ICSE Class 10 Maths Selina Solution
• Chapter 12 Reflection

Selina Solutions Concise Maths Class 10 Chapter 12 Reflection

This Chapter gives a brief on co-ordinate geometry and other important concepts like the reflection of a point in different co-ordinate axes, origin and with respect to a line. It is very important for the students to have strong command about the concepts covered in each chapter of Class 10 as it’s a turning point in a student’s life. To make the process easier, BYJU’S has created the Selina Solutions for Class 10 Mathematics which is a valuable resource for students. After all, it’s advantageous to obtain a good score in a subject like Mathematics. The solutions are made available in PDF format so that the students can download it. The Selina Solutions for Class 10 Mathematics Chapter 12 Reflection PDF are given below.

Selina Solutions Concise Maths Class 10 Chapter 12 Reflection Download PDF

Exercises of Selina Solutions Concise Maths Class 10 Chapter 12 Reflection

Exercise 12(A) Solutions

Exercise 12(B) Solutions

Access Selina Solutions Concise Maths Class 10 Chapter 12 Reflection

Exercise 12(A) Page No: 165

1. Complete the following table:

2. A point P is its own image under the reflection in a line l. Describe the position of point the P with respect to the line l.

As, the image of the point P is the same point under the reflection in the line l we can say, point P is an invariant point.

Thus, the position of point P remains unaltered.

3. State the co-ordinates of the following points under reflection in x-axis:

(ii) (-5, 4)

(iii) (0, 0)

The co-ordinates of the given point under reflection in the x-axis are (3, -2).

The co-ordinates of the given point under reflection in the x-axis are (-5, -4).

The co-ordinates of the given point under reflection in the x-axis are (0, 0).

4. State the co-ordinates of the following points under reflection in y-axis:

(i) (6, -3)

(ii) (-1, 0)

(iii) (-8, -2)

The co-ordinates of the given point under reflection in the y-axis are (-6, -3).

The co-ordinates of the given point under reflection in the y-axis are (1, 0).

The co-ordinates of the given point under reflection in the y-axis are (8, -2).

5. State the co-ordinates of the following points under reflection in origin:

(i) (-2, -4)

(ii) (-2, 7)

The co-ordinates of the given point under reflection in origin are (2, 4).

The co-ordinates of the given point under reflection in origin are (2, -7).

The co-ordinates of the given point under reflection in origin are (0, 0).

6. State the co-ordinates of the following points under reflection in the line x = 0:

(i) (-6, 4)

(ii) (0, 5)

(iii) (3, -4)

The co-ordinates of the given point under reflection in the line x = 0 are (6, 4).

The co-ordinates of the given point under reflection in the line x = 0 are (0, 5).

The co-ordinates of the given point under reflection in the line x = 0 are (-3, -4).

7. State the co-ordinates of the following points under reflection in the line y = 0:

(i) (-3, 0)

(ii) (8, -5)

(iii) (-1, -3)

The co-ordinate of the given point under reflection in the line y = 0 is (-3, 0).

The co-ordinate of the given point under reflection in the line y = 0 is (8, 5).

The co-ordinate of the given point under reflection in the line y = 0 is (-1, 3).

8. A point P is reflected in the x-axis. Co-ordinates of its image are (-4, 5).

(i) Find the co-ordinates of P.

(ii) Find the co-ordinates of the image of P under reflection in the y-axis.

(i) As, M x  (-4, -5) = (-4, 5)

Hence, the co-ordinates of P are (-4, -5).

(ii) Co-ordinates of the image of P under reflection in the y-axis (4, -5).

9. A point P is reflected in the origin. Co-ordinates of its image are (-2, 7).

(ii) Find the co-ordinates of the image of P under reflection in the x-axis.

(i) As, M O  (2, -7) = (-2, 7)

Hence, the co-ordinates of P are (2, -7).

(ii) Co-ordinates of the image of P under reflection in the x-axis (2, 7)

Exercise 12(B) Page No: 165

1. Attempt this question on graph paper.

(a) Plot A (3, 2) and B (5, 4) on graph paper. Take 2 cm = 1 unit on both the axes.

(b) Reflect A and B in the x-axis to A’ and B’ respectively. Plot these points also on the same graph paper.

(c) Write down:

(i) the geometrical name of the figure ABB’A’;

(ii) the measure of angle ABB’;

(iii) the image of A” of A, when A is reflected in the origin.

(iv) the single transformation that maps A’ to A”.

(i) From the graph, it’s clearly seen that ABB’A’ is an isosceles trapezium.

(ii) The measure of angle ABB’ is 45°.

(iii) A” = (-3, -2)

(iv) Single transformation that maps A’ to A” is the reflection in y-axis.

2. Points (3, 0) and (-1, 0) are invariant points under reflection in the line L 1 ; points (0, -3) and (0, 1) are invariant points on reflection in line L 2 .

(i) Name or write equations for the lines L 1  and L 2 .

(ii) Write down the images of the points P (3, 4) and Q (-5, -2) on reflection in line L 1 . Name the images as P’ and Q’ respectively.

(iii) Write down the images of P and Q on reflection in L 2 . Name the images as P” and Q” respectively.

(iv) State or describe a single transformation that maps P’ onto P”.

(i) We know that, every point in a line is invariant under the reflection in the same line.

As the points (3, 0) and (-1, 0) lie on the x-axis.

Thus, (3, 0) and (-1, 0) are invariant under reflection in x-axis.

Therefore, the equation of line L 1  is y = 0.

Similarly, (0, -3) and (0, 1) are also invariant under reflection in y-axis.

Therefore, the equation of line L 2  is x = 0.

(ii) P’ = Image of P (3, 4) in L 1  = (3, -4)

And, Q’ = Image of Q (-5, -2) in L 1  = (-5, 2)

(iii) P” = Image of P (3, 4) in L 2  = (-3, 4)

And, Q” = Image of Q (-5, -2) in L 2  = (5, -2)

(iv) Single transformation that maps P’ onto P” is reflection in origin.

3. (i) Point P (a, b) is reflected in the x-axis to P’ (5, -2). Write down the values of a and b.

(ii) P” is the image of P when reflected in the y-axis. Write down the co-ordinates of P”.

(iii) Name a single transformation that maps P’ to P”.

(i) As, M x  (x, y) = (x, -y)

P’ (5, -2) = reflection of P (a, b) in x-axis.

Hence, the co-ordinates of P are (5, 2).

Thus, a = 5 and b = 2.

(ii) P” = image of P (5, 2) reflected in y-axis = (-5, 2)

(iii) Single transformation that maps P’ to P” is the reflection in origin.

4. The point (-2, 0) on reflection in a line is mapped to (2, 0) and the point (5, -6) on reflection in the same line is mapped to (-5, -6).

(i) State the name of the mirror line and write its equation.

(ii) State the co-ordinates of the image of (-8, -5) in the mirror line.

(i) We know that, reflection of a point (x, y) in y-axis is (-x, y).

So, the point (-2, 0) when reflected in y-axis is mapped to (2, 0).

Hence, the mirror line is the y-axis and it’s equation is x = 0.

(ii) The co-ordinates of the image of (-8, -5) in the mirror line (i.e., y-axis) are (8, -5).

5. The points P (4, 1) and Q (-2, 4) are reflected in line y = 3. Find the co-ordinates of P’, the image of P and Q’, the image of Q.

The line y = 3 is a line parallel to x-axis and at a distance of 3 units from it.

Let’s mark the points P (4, 1) and Q (-2, 4).

Now from P, draw a straight line perpendicular to line CD and produce. Mark a point P’ on this line which is at the same distance above CD as P is below it.

Thus, the co-ordinates of P’ are (4, 5).

Similarly, from Q, draw a line perpendicular to CD and mark point Q’ which is at the same distance below CD as Q is above it.

Hence, the co-ordinates of Q’ are (-2, 2).

6. A point P (-2, 3) is reflected in line x = 2 to point P’. Find the coordinates of P’.

The line x = 2 is a line parallel to y-axis and at a distance of 2 units from it.

Let’s mark the point P (-2, 3).

From P, draw a straight line perpendicular to line CD and produce. Mark a point on this line which is at the same distance to the right of CD as P is to the left of it.

Hence, the co-ordinates of P’ are (6, 3).

7. A point P (a, b) is reflected in the x-axis to P’ (2, -3). Write down the values of a and b. P” is the image of P, reflected in the y-axis. Write down the co-ordinates of P”. Find the co-ordinates of P”’, when P is reflected in the line, parallel to y-axis, such that x = 4.

A point P (a, b) is reflected in the x-axis to P’ (2, -3).

We know that, M x  (x, y) = (x, -y)

Hence, the co-ordinates of P are (2, 3).

And thus, a = 2 and b = 3.

P” = Image of P reflected in the y-axis = (-2, 3)

P”’ = Reflection of P in the line (x = 4, a line parallel to y-axis and at a distance of 4 units from it) = (6, 3)

8. Points A and B have co-ordinates (3, 4) and (0, 2) respectively. Find the image:

(a) A’ of A under reflection in the x-axis.

(b) B’ of B under reflection in the line AA’.

(c) A” of A under reflection in the y-axis.

(d) B” of B under reflection in the line AA”.

(a) A’ = Image of A under reflection in the x-axis = (3, -4)

(b) B’ = Image of B under reflection in the line AA’ (x = 3) = (6, 2)

(c) A” = Image of A under reflection in the y-axis = (-3, 4)

(d) B” = Image of B under reflection in the line AA” (y = 4) = (0, 6)

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