Question

A triangle is dilated with the center of dilation at point U. Point E is a vertex of the triangle and point E ′ E' is the corresponding vertex of the image. If UE = 2 centimeters and U ′ E ′ = 10 U'E'=10 centimeters, what is the scale factor?

Answer 1

Answer: $scale\ factor=5$

Step-by-step explanation:

By definition, a Dilation is a transformation in which the image has the same shape as the pre-image but  size changes.

The center of dilation is a fixed point in the plane, and the scale factor is the ratio of the corresponding sides of the image to the pre-image.

Based on the information provided in the exercise, you know that:

$UE = 2\ cm\\\\U'E'=10\ cm$

Thererefore, you can determine that the scale factor is:

$scale\ factor=\frac{10\ cm}{2\ cm}\\\\scale\ factor=5$