Question

triangle xyz is dilated by a scale factor of \\( \frac { 1 } { 2 } \\) to form triangle xyz. what is the measure of side yz? answer attempt 1 out of 2 submit answer

Explanation:

Step1: Recall the dilation formula

When a figure is dilated, the length of a side of the new figure \(s'\) is given by \(s'=s\times k\), where \(s\) is the length of the corresponding side of the original figure and \(k\) is the scale factor.

Step2: Identify the values

Here, the original side length \(s = YZ=40\) (from the triangle \(XYZ\)), and the scale factor \(k=\frac{1}{2}\).

Step3: Calculate \(Y'Z'\)

Substitute the values into the formula: \(Y'Z'=YZ\times\frac{1}{2}\). So, \(Y'Z' = 40\times\frac{1}{2}\).
Using the multiplication \(40\times\frac{1}{2}=\frac{40}{1}\times\frac{1}{2}\). By the rule of fraction - multiplication \(\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}\), we have \(\frac{40\times1}{1\times2}=\frac{40}{2} = 20\).

Answer:

\(20\)