Question

triangle xyz is dilated by a scale factor of $\frac{1}{4}$ to form triangle xyz. side yz measures 34. what is the measure of side yz?

Explanation:

Step1: Recall the formula for dilation

When a figure is dilated, the length of a side of the new figure is equal to the length of the corresponding side of the original figure multiplied by the scale factor. So, \(Y'Z'=YZ\times\text{scale factor}\).

Step2: Substitute the given values

We know that \(YZ = 34\) and the scale factor \(k=\frac{1}{4}\). Then \(Y'Z'=34\times\frac{1}{4}\).
Calculate \(34\times\frac{1}{4}=\frac{34}{4}=\frac{17}{2}=8.5\)

Answer:

\(8.5\)