Question

A dilation with center C and a scale factor k maps X onto Y. Find

k for each dilation. Then determine whether each dilation is an
enlargement, a reduction, or a congruence transformation.
CY=15, CX = 10
Find k for the dilation mapping X onto Y. Determine whether it is an enlargement, a reduction, or a congruence transformation.

Answer 1

The scale factor k for the dilation mapping X onto Y is 1.5, which indicates an enlargement since k is greater than 1.

Step-by-step explanation:

To find the scale factor k for the dilation mapping point X onto point Y, you can use the ratio of the distance from the center C to Y over the distance from the center C to X. In mathematical terms:

k = CY / CX

In this problem, CY = 15 and CX = 10. Therefore:

k = 15 / 10 = 1.5

This means that the scale factor is 1.5. Since k is greater than 1, the dilation is an enlargement, because the image Y is larger than the pre-image X by a factor of 1.5.