[G.SRT.1] Similarity, Right Triangles, and Trigonometry #1

Looks like it worked. Can you see that all the points are twice as far from H as they were before?

Example 2

In the following picture, the origin is the center of dilation. Perform the dilation with a scale factor of 3.

Here we have

  • two shapes, a triangle and a trapezoid

    • these are our shapes that will be dilated

  • point H, which is our center of dilation

    • The center of dilation is only point that doesn't move. Everything else expands out from the center of dilation.

  • and we've been told to use 2 for our scale factor

    • A scale factor tells you how much everything is going to dilate (expand). A scale factor of 2 means every image point will be 2x as far from the center of rotation

Let's see what happens.

Objective

Common Core Text:

    • [G.SRT.1] Verify experimentally the properties of dilations given by a center and a scale factor.

    • [G.SRT.1.a] A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

      • [G.SRT.1.b] The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

Said Differently:

    • Draw dilations given a preimage, center of dilation, and a scale factor.

Example

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Explanation

Introduction

We've already discussed three types of transformations (rotations, reflections, and translations). Now we're going to learn about another type of transformation called a dilation.

In a dictionary,

  • Dilation: "...to become wider, larger, or more open."

In math, a dilation expands everything out around a point. Lets take a look at an example.

Example 1

Perform a dilation on triangle ABC and trapezoid DEFG with center of dilation H and a scale factor of 2.

We get

In our last example, we'll look at what happens when the scale factor is less than 1

Example 3

In the following picture, the origin is the center of dilation. Perform the dilation with a scale factor of 0.5.

Well it sure did. These dilations with scale factors smaller than 1 are often called contractions.

Making Dilations Using Geogebra

Constructing Dilations With Compass and Straightedge

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Practice your skills

0.5 is the same as 1/2, so we'd expect everything to get twice as small. Lets see if it does.