How Shapes Change: Triangle Dilation from the Center

Chelsea

6/26/2023

Arithmetic

Similarity

•

Jun 26, 2023

•

4 pages

How Shapes Change: Triangle Dilation from the Center

Name: Knowunity
Brand: Knowunity

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 $-2,-2$ , B $-6,-2$ , and C $-6,2$ 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.

Page 3: Determining Scale Factors

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

Example: When point M $-3,5$ is dilated to M' $-6,10$ , 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.

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 A(2,1) to A'(6,3), 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.

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 $-4,1$ , E $2,3$ , and F $2,1$ is dilated by a factor of 3 using the origin, resulting in D' $-12,3$ , E'(6,9), and F'(6,3).

Highlight: The rule for dilation can be written as (x,y) → (kx,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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You can download the app in the Google Play Store and in the Apple App Store.

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Arithmetic

•

Jun 26, 2023

•

4 pages

How Shapes Change: Triangle Dilation from the Center

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

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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 $-2,-2$ , B $-6,-2$ , and C $-6,2$ 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.

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Page 3: Determining Scale Factors

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

Example: When point M $-3,5$ is dilated to M' $-6,10$ , 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.

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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 A(2,1) to A'(6,3), 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.

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 $-4,1$ , E $2,3$ , and F $2,1$ is dilated by a factor of 3 using the origin, resulting in D' $-12,3$ , E'(6,9), and F'(6,3).

Highlight: The rule for dilation can be written as (x,y) → (kx,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?

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.

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

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Thomas R

iOS user

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

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

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

Elisha

iOS user

Paul T

iOS user

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Thomas R

iOS user

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

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

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

Elisha

iOS user

Paul T

iOS user