[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.