Dilations

A dilation is a similarity transformation, meaning the preimage and image side lengths are proportional and corresponding angles are congruent. Every dilation has a center and a scale factor. There are two types of dilations, enlargements and reductions. You will explore and practice the properties of dilations in this activity.

1. Plot the points D(2,4), E(4,5), F(5,4)

2. Connect points D, E, and F to make

3. Next you will make an enlargement of by a scale factor of 2. To do this we will use scalar multiplication. Essentially we will multiply every coordinate by 2. This can be modeled using a 2x3 matrix where row 1 are x values, row 2 are y values, column 1 is point D, column 2 is point E, and column 3 is point F.

=

We now have the image points D’(4,8), E’(8,10), and F’(10,8)

4. Plot points D’, E’, and F’ and connect points to make

5. Create a new triangle of your choosing. Label the points A, B, C.

6. Use scalar multiplication to dilate the triangle by a scale factor of ½.

7. Graph the resulting triangle

8. Using the distance formula, find the distance of each segment to the nearest mm.

AB=	A’B’=
BC=	B’C’=
CA=	C’A’=

9. Find the following ratios (scale factors):

10. With a protractor, measure the following angles:

11. A Dilation is a similarity transformation. Explain how your findings in #9 and #10 demonstrate a similarity transformation.