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: Use the property of similar figures

Since rectangle \(WXYZ\) is dilated to create \(W'X'Y'Z'\), the two rectangles are similar. For similar figures, the ratios of corresponding sides are equal. Let \(W'X' = x\). The ratio of the sides can be set up using the segments from the center of dilation.

Step2: Set up the proportion

We have the proportion \(\frac{W'X'}{WX}=\frac{OW'}{OW}\). We know \(OW' = 1.5\), \(OW=1.5 + 3=4.5\), and \(WX = 4.5\). Substituting into the proportion: \(\frac{x}{4.5}=\frac{1.5}{4.5}\).

Step3: Solve the proportion for \(x\)

Cross - multiply: \(4.5x=1.5\times4.5\). Then \(x = 1.5\) units.

Answer:

1.5 units