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

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

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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.

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