Exercise 35 Page 700

To locate the center of dilation P, we will draw lines that pass through the corresponding vertices of the preimage and image. The point where these lines intersect is the center of the dilation.

We found that the center of the dilation is the common vertex of the rectangles. Now, since the dilated image is larger than the preimage, the dilation is an enlargement. This means that the scale factor k should be greater than 1.

k > 1 To find the scale factor, we will find the ratio of a length in the image to a corresponding length in the preimage. Let's measure the lengths of the rectangles.

We see that the length of the small rectangle is 1.5 cm, and that the length of the large rectangle is 3.3 cm. Using these lengths, we can find the scale factor of the dilation.

k=image length/preimage length

SubstituteValues

Substitute values

k=3.3/1.5

ExpandFrac

a/b=a * 10/b * 10

k=33/15

ReduceFrac

a/b=.a /3./.b /3.

k=11/5

The scale factor of the dilation is 115.