Question

A quadrilateral with vertices at A(4, -4), B(4, -16), C(12, -16), and D(12, -4) has been dilated with a center at the origin. The image of D, point , has coordinates (36, -12). What is the scale factor of the dilation?

A. 1/9
B. 1/3
C. 3
D. 9

Answer 1

The scale factor of the dilation is found by dividing the image's x-coordinate by the original x-coordinate of point D, which is 3.

Step-by-step explanation:

To find the scale factor of the dilation, we can compare the coordinates of the original point D(12, -4) with its image's coordinates (36, -12). We must determine how much the x-coordinate and y-coordinate have been scaled by.

Looking at the x-coordinate, the formula for determining the scale factor (k) is:

Original x-coordinate * k = Image's x-coordinate
12 * k = 36

Solving for k gives us:

k = 36 / 12
k = 3

Therefore, the scale factor is C. 3.