Question

rectangle wxyz was dilated to create wxyz. what is wx? 0.5 units 1.2 units 1.5 units 1.8 units

Explanation:

Step1: Find the scale factor

The scale factor \(k\) of a dilation is given by the ratio of the corresponding side lengths of the image and the pre - image. For the sides \(GZ'\) and \(GZ\), \(k=\frac{GZ'}{GZ}\). Here, \(GZ' = 1.5\) and \(GZ=1.5 + 7.5=9\). So, \(k=\frac{1.5}{9}=\frac{1}{6}\).

Step2: Calculate \(W'X'\)

Since \(WX = 3\) and the scale factor \(k=\frac{1}{6}\), using the formula for dilation \(W'X'=k\times WX\). Substitute \(k = \frac{1}{6}\) and \(WX = 3\) into the formula: \(W'X'=\frac{1}{6}\times3 = 0.5\).

Answer:

0.5 units