Understanding rigid motion in geometryand transformations - a comprehensive... Show more
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Feb 12, 2026
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Fun with Reflection and Translation in Geometry: Worksheets & Examples for Kids
Colleensasser
@colleeflowerr
1 / 9
Page 2: Advanced Reflection Examples
This page expands on reflection concepts with multiple examples across different lines of reflection.
Example: When reflecting across x=4:
- Point J(1,-1) becomes J'(7,-1)
- Point K(2,3) becomes K'(6,3)
- Point L(3,-2) becomes L'(5,-2)
Highlight: Key rules for different reflection lines:
- For x=a line: y-coordinate stays the same
- For y=b line: x-coordinate stays the same
- For y=x line: x and y coordinates switch places
Page 3: Complex Reflections
This page covers more advanced reflection examples, particularly focusing on diagonal reflections and their rules.
Example: For reflection across y=-x:
- Point S(-1,-6) becomes S'(6,1)
- Point T(0,-3) becomes T'(3,0)
- Point U(3,-4) becomes U'(4,-3)
Highlight: When reflecting across y=-x, coordinates switch places and change signs.
Page 4: Introduction to Translations
This page introduces translations as another type of rigid motion.
Definition: A translation is a transformation that slides a figure vertically and/or horizontally without changing its size or shape.
Vocabulary: Translation notation: (x,y) → or <h,k>
- h represents horizontal shift
- k represents vertical shift
Example: Translation T<5,7>:
- Point D(-3,3) becomes D'(4,7)
- Point E(0,2) becomes E'(7,6)
- Point F(-1,-3) becomes F'(6,7)
Page 5: Composition of Transformations
This page explores how multiple transformations can be combined.
Definition: A composition of rigid motions involves applying two or more transformations sequentially.
Example: Reflecting across x-axis followed by translation T<9,-1>:
- Point X(-3,1) becomes X'(-3,-1) then X"(6,-8)
- Point Y(-2,1) becomes Y'(-2,-1) then Y"(7,-2)
Highlight: When combining transformations, the order of operations matters and affects the final result.
Page 6: Introduction to Rotations
This page introduces rotation as a rigid motion, focusing on rotations around the origin.
Definition: Rotation rules around the origin:
- 90° CCW: (x,y) →
- 180°: (x,y) →
- 270° CCW: (x,y) →
Example: 90° rotation about the origin:
- Point A(3,5) becomes A'(-5,3)
- Point B(1,7) becomes B'(-7,1)
Page 7: Advanced Rotations
This page explores more complex rotation examples and combinations with other transformations.
Example: 270° rotation about the origin:
- Point A(2,7) becomes A'(-7,2)
- Point B(6,5) becomes B'(-5,6)
Highlight: Multiple transformations can be combined, such as translation followed by rotation or reflection followed by rotation.
Page 8: Rotations Around Points
This page explains how to perform rotations around points other than the origin.
Definition: Four-step process for rotating around a point:
- Write original points
- Subtract point of rotation
- Apply rotation rules
- Add back point of rotation
Example: 180° rotation around point (1,1):
- Original point F(1,2)
- Subtract (1,1): (0,1)
- Apply rotation: (0,-1)
- Add (1,1): F'(1,0)
Page 9: Final Rotation Examples
This page provides additional examples of rotations around specific points.
Example: 90° CCW rotation around point (0,1):
- Point G(-3,-2) becomes G'(3,-2)
- Point F(-3,-5) becomes F'(6,-2)
- Point H(0,-1) becomes H'(7,1)
Highlight: The process demonstrates how complex rotations can be broken down into manageable steps using coordinate geometry.
Page 1: Introduction to Reflections
This page introduces the fundamental concepts of rigid motion in geometry and reflections. A reflection involves flipping a figure across a line while maintaining equal distances from the line of reflection.
Definition: A rigid motion is a transformation that preserves both length and angle measurements.
Vocabulary: A reflection is a flip over a line called the line of reflection, where each point and its image are equidistant from the line.
Example: When reflecting point A(-4,2) across the x-axis, its image becomes A'(-4,-2), demonstrating how the y-coordinate changes sign while the x-coordinate remains the same.
Highlight: Common lines of reflection include:
- x-axis and y-axis
- Vertical lines and horizontal lines
- Diagonal lines
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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Fun with Reflection and Translation in Geometry: Worksheets & Examples for Kids
Colleensasser
@colleeflowerr
Understanding rigid motion in geometry and transformations - a comprehensive guide covering reflections, translations, and rotations with detailed examples and rules.
- Rigid motions preserve both length and angle measurements while transforming geometric figures
- Reflectionsinvolve flipping figures across a line... Show more
Page 2: Advanced Reflection Examples
This page expands on reflection concepts with multiple examples across different lines of reflection.
Example: When reflecting across x=4:
- Point J(1,-1) becomes J'(7,-1)
- Point K(2,3) becomes K'(6,3)
- Point L(3,-2) becomes L'(5,-2)
Highlight: Key rules for different reflection lines:
- For x=a line: y-coordinate stays the same
- For y=b line: x-coordinate stays the same
- For y=x line: x and y coordinates switch places
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Page 3: Complex Reflections
This page covers more advanced reflection examples, particularly focusing on diagonal reflections and their rules.
Example: For reflection across y=-x:
- Point S(-1,-6) becomes S'(6,1)
- Point T(0,-3) becomes T'(3,0)
- Point U(3,-4) becomes U'(4,-3)
Highlight: When reflecting across y=-x, coordinates switch places and change signs.
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Page 4: Introduction to Translations
This page introduces translations as another type of rigid motion.
Definition: A translation is a transformation that slides a figure vertically and/or horizontally without changing its size or shape.
Vocabulary: Translation notation: (x,y) → or <h,k>
- h represents horizontal shift
- k represents vertical shift
Example: Translation T<5,7>:
- Point D(-3,3) becomes D'(4,7)
- Point E(0,2) becomes E'(7,6)
- Point F(-1,-3) becomes F'(6,7)
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Page 5: Composition of Transformations
This page explores how multiple transformations can be combined.
Definition: A composition of rigid motions involves applying two or more transformations sequentially.
Example: Reflecting across x-axis followed by translation T<9,-1>:
- Point X(-3,1) becomes X'(-3,-1) then X"(6,-8)
- Point Y(-2,1) becomes Y'(-2,-1) then Y"(7,-2)
Highlight: When combining transformations, the order of operations matters and affects the final result.
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Page 6: Introduction to Rotations
This page introduces rotation as a rigid motion, focusing on rotations around the origin.
Definition: Rotation rules around the origin:
- 90° CCW: (x,y) →
- 180°: (x,y) →
- 270° CCW: (x,y) →
Example: 90° rotation about the origin:
- Point A(3,5) becomes A'(-5,3)
- Point B(1,7) becomes B'(-7,1)
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Page 7: Advanced Rotations
This page explores more complex rotation examples and combinations with other transformations.
Example: 270° rotation about the origin:
- Point A(2,7) becomes A'(-7,2)
- Point B(6,5) becomes B'(-5,6)
Highlight: Multiple transformations can be combined, such as translation followed by rotation or reflection followed by rotation.
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Page 8: Rotations Around Points
This page explains how to perform rotations around points other than the origin.
Definition: Four-step process for rotating around a point:
- Write original points
- Subtract point of rotation
- Apply rotation rules
- Add back point of rotation
Example: 180° rotation around point (1,1):
- Original point F(1,2)
- Subtract (1,1): (0,1)
- Apply rotation: (0,-1)
- Add (1,1): F'(1,0)
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Page 9: Final Rotation Examples
This page provides additional examples of rotations around specific points.
Example: 90° CCW rotation around point (0,1):
- Point G(-3,-2) becomes G'(3,-2)
- Point F(-3,-5) becomes F'(6,-2)
- Point H(0,-1) becomes H'(7,1)
Highlight: The process demonstrates how complex rotations can be broken down into manageable steps using coordinate geometry.
Sign up to see the contentIt's free!
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Page 1: Introduction to Reflections
This page introduces the fundamental concepts of rigid motion in geometry and reflections. A reflection involves flipping a figure across a line while maintaining equal distances from the line of reflection.
Definition: A rigid motion is a transformation that preserves both length and angle measurements.
Vocabulary: A reflection is a flip over a line called the line of reflection, where each point and its image are equidistant from the line.
Example: When reflecting point A(-4,2) across the x-axis, its image becomes A'(-4,-2), demonstrating how the y-coordinate changes sign while the x-coordinate remains the same.
Highlight: Common lines of reflection include:
- x-axis and y-axis
- Vertical lines and horizontal lines
- Diagonal lines
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user