Question

Using point Q as the center of dilation.

Point Q is the center of dilation. Line segment A B is dilated to create line segment A prime B prime. The length of Q A is 1.25 and the length of A A prime is 1.25.

What is the scale factor?

1
1.25
2
2.5

Answer 1

(c) 2

Explanation:

The dilation scale factor multiplies the distance from the center of dilation.

Distance from Q

We are given that QA = 1.25, and that AA' = 1.25. By the segment sum theorem, we have ...

QA' = QA +AA'

QA' = 1.25 +1.25 = 2.50

Scale factor

The scale factor multiplies the original distance:

QA' = k·QA . . . . . . . . . . where k is the dilation scale factor

2.50 = k·1.25 . . . . . . . . using the known lengths

2.50/1.25 = k = 2 . . . . divide by the coefficient of k

The scale factor is 2.