Master

Dilation

Master dilation with interactive lessons and practice problems! Designed for students like you!

Learn

Get the basics

Practice

Apply your skills

Master

Achieve excellence

Dilation

Study Guide

Key Definition

A dilation is a transformation that changes the size of a figure, requiring a center point and a scale factor $k$. If $|k| > 1$, it is an enlargement; if $|k| < 1$, it is a reduction.

Important Notes

Dilations preserve angle measure and collinearity but not distance.
The center of a dilation is always its own image.
When $k$ is positive, the image is on the same side of the center.
When $k$ is negative, the image is on the opposite side.
Dilations always produce similar figures.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

$(x, y) → (kx, ky)$ represents the coordinate rule for dilation

Remember to use proper notation when solving problems

Why It Works

Dilations create similar figures by scaling distances from a center point by a scale factor $k$.

Remember

For dilations, if $|k| > 1$, the figure enlarges, and if $|k| < 1$, it reduces.

Quick Reference

Scale Factor:$k$

Enlargement Condition:$|k| > 1$

Reduction Condition:$|k| < 1$

Understanding Dilation

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Dilation involves resizing a figure proportionally from a center point using a scale factor $k$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

If a dilation has a scale factor of $k = 2$, what happens to the figure?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine a photo is enlarged to twice its size using a scale factor of $k = 2$.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Consider a triangle undergoing dilation with $k = -0.5$. What happens to its orientation?

Challenge Quiz

Single Choice Quiz

Advanced

A figure is dilated with a scale factor $k = -3$. What is true about the dilation?

Recap

Watch & Learn

Review key concepts and takeaways