Question

Polygon ABCD, shown in the figure, is dilated by a scale factor of 8 with the origin as the center of dilation, resulting in the image A′B′C′D′ hat is the slope of C'D'

Answer 1

Dilation preserves the parallel lines, it means that the image line C'D' of the line CD are parallel each to other and their slopes are the same. So you have only to find the slope of CD.

If line is passing through the points $(x_1,y_1)$ and $(x_2,y_2)$, the slope is

$\dfrac{y_2-y_1}{x_2-x_1}.$

From the diagram you can find coordinates of points C and D:

C(5,4), D(4,2).

Thus, the slope of CD is

$\dfrac{2-4}{4-5}=2.$

Answer: 2.

Answer 2

Since the transformation done is dilation with dilation factor of 8 with the center as the dilation the coordinates of C' is (45, 36) and of D' is (36, 18). So, the slope is
m = (18 - 36) / (36 - 45)
m = 2
This slope is also the slope between C and D.