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How Shapes Change: Triangle Dilation from the Center

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Arithmetic

Transformations

Dilations

44

•

Jun 26, 2023

•

4 pages

How Shapes Change: Triangle Dilation from the Center

user profile picture

Chelsea

@zuncho

Triangle dilation scale factor explanationand coordinate geometry transformations guide... Show more

1 3 Triangle DEFhas vertices D(-4,1), E(2, 3), and F(2, 1) and is dilated by a factor of 3 using the origin as the point of dilation. The di

Page 2: Scale Factors and Their Effects

This page explores how scale factors affect dilations and the relationships between original and dilated figures.

Definition: A scale factor between 0 and 1 results in a reduction, while a scale factor greater than 1 results in an enlargement.

Example: Triangle ABC with vertices A−2,−2-2,-2, B−6,−2-6,-2, and C−6,2-6,2 is dilated by a factor of ½, producing a reduction.

Highlight: When dilating figures, all corresponding angles remain congruent while side lengths are multiplied by the scale factor.

1 3 Triangle DEFhas vertices D(-4,1), E(2, 3), and F(2, 1) and is dilated by a factor of 3 using the origin as the point of dilation. The di

Page 3: Determining Scale Factors

This page focuses on calculating scale factors from given coordinates and understanding transformation sequences.

Example: When point M−3,5-3,5 is dilated to M'−6,10-6,10, the scale factor can be found by comparing corresponding coordinates.

Definition: The scale factor is the ratio of the image's distance from the center to the pre-image's distance from the center.

Highlight: Complex transformations may involve both dilations and translations in sequence.

1 3 Triangle DEFhas vertices D(-4,1), E(2, 3), and F(2, 1) and is dilated by a factor of 3 using the origin as the point of dilation. The di

Page 4: Advanced Dilation Practice

This page provides extensive practice with various scale factors and coordinate calculations.

Example: Triangle ABC is dilated by a factor of 3, transforming A2,12,1 to A'6,36,3, demonstrating an enlargement.

Highlight: Scale factors can be determined by comparing corresponding coordinates of original and dilated points.

Vocabulary: Corresponding points are points that map to each other in a transformation.

1 3 Triangle DEFhas vertices D(-4,1), E(2, 3), and F(2, 1) and is dilated by a factor of 3 using the origin as the point of dilation. The di

Page 1: Introduction to Dilations and Transformations

This page introduces fundamental concepts of dilations and transformations through practical examples. Students learn to work with coordinate points and apply dilation rules.

Definition: A dilation is a transformation that produces a similar figure by multiplying all distances from a center point by a scale factor.

Example: Triangle DEF with vertices D−4,1-4,1, E2,32,3, and F2,12,1 is dilated by a factor of 3 using the origin, resulting in D'−12,3-12,3, E'6,96,9, and F'6,36,3.

Highlight: The rule for dilation can be written as x,yx,y → kx,kykx,ky where k is the scale factor.

Vocabulary: Pre-image refers to the original figure, while image refers to the transformed figure.



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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 THE SCHOOLGPT. 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 THE SCHOOLGPT. 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

Subjects

Arithmetic

Transformations

Dilations

 

Arithmetic

•

44

•

Jun 26, 2023

•

4 pages

How Shapes Change: Triangle Dilation from the Center

user profile picture

Chelsea

@zuncho

Triangle dilation scale factor explanation and coordinate geometry transformations guide for students learning about geometric transformations and similarity.

  • Learn how to perform dilation using origin as center with various scale factors
  • Understand how to calculate coordinates of dilated figures and... Show more

1 3 Triangle DEFhas vertices D(-4,1), E(2, 3), and F(2, 1) and is dilated by a factor of 3 using the origin as the point of dilation. The di

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 2: Scale Factors and Their Effects

This page explores how scale factors affect dilations and the relationships between original and dilated figures.

Definition: A scale factor between 0 and 1 results in a reduction, while a scale factor greater than 1 results in an enlargement.

Example: Triangle ABC with vertices A−2,−2-2,-2, B−6,−2-6,-2, and C−6,2-6,2 is dilated by a factor of ½, producing a reduction.

Highlight: When dilating figures, all corresponding angles remain congruent while side lengths are multiplied by the scale factor.

1 3 Triangle DEFhas vertices D(-4,1), E(2, 3), and F(2, 1) and is dilated by a factor of 3 using the origin as the point of dilation. The di

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 3: Determining Scale Factors

This page focuses on calculating scale factors from given coordinates and understanding transformation sequences.

Example: When point M−3,5-3,5 is dilated to M'−6,10-6,10, the scale factor can be found by comparing corresponding coordinates.

Definition: The scale factor is the ratio of the image's distance from the center to the pre-image's distance from the center.

Highlight: Complex transformations may involve both dilations and translations in sequence.

1 3 Triangle DEFhas vertices D(-4,1), E(2, 3), and F(2, 1) and is dilated by a factor of 3 using the origin as the point of dilation. The di

Page 4: Advanced Dilation Practice

This page provides extensive practice with various scale factors and coordinate calculations.

Example: Triangle ABC is dilated by a factor of 3, transforming A2,12,1 to A'6,36,3, demonstrating an enlargement.

Highlight: Scale factors can be determined by comparing corresponding coordinates of original and dilated points.

Vocabulary: Corresponding points are points that map to each other in a transformation.

1 3 Triangle DEFhas vertices D(-4,1), E(2, 3), and F(2, 1) and is dilated by a factor of 3 using the origin as the point of dilation. The di

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Introduction to Dilations and Transformations

This page introduces fundamental concepts of dilations and transformations through practical examples. Students learn to work with coordinate points and apply dilation rules.

Definition: A dilation is a transformation that produces a similar figure by multiplying all distances from a center point by a scale factor.

Example: Triangle DEF with vertices D−4,1-4,1, E2,32,3, and F2,12,1 is dilated by a factor of 3 using the origin, resulting in D'−12,3-12,3, E'6,96,9, and F'6,36,3.

Highlight: The rule for dilation can be written as x,yx,y → kx,kykx,ky where k is the scale factor.

Vocabulary: Pre-image refers to the original figure, while image refers to the transformed figure.

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?

You have the choice, we offer a 100% secure payment via PayPal or an Amazon gift card. There is no limit to how much you can earn.

Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.9/5

App Store

4.8/5

Google Play

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 THE SCHOOLGPT. 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 THE SCHOOLGPT. 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