Question

in the dilation shown, the larger figure represents the original image and the smaller figure represents the resulting image. what is the scale factor for this dilation?
a. $\frac{1}{2}$
b. $\frac{1}{2}$
c. 2
d. - 3

Explanation:

Step1: Select corresponding side lengths

Choose a side - length of the original and dilated figures. For example, the base of the larger (original) triangle is 2 units (from \(x = 3\) to \(x = 5\)) and the base of the smaller (dilated) triangle is 1 unit (from \(x = 2\) to \(x = 3\)).

Step2: Calculate the scale factor

The scale factor \(k\) of a dilation from the original figure to the dilated figure is given by the formula \(k=\frac{\text{length of corresponding side in dilated figure}}{\text{length of corresponding side in original figure}}\). So, \(k = \frac{1}{2}\).

Answer:

A. \(\frac{1}{2}\)