Question

triangle abc is dilated by a scale factor of $\frac{1}{2}$ to form triangle abc. what is the measure of side ca?

Explanation:

Step1: Recall the property of dilation

When a figure is dilated, the length of each side of the new figure is the length of the corresponding side of the original figure multiplied by the scale factor.

Step2: Identify the corresponding side and calculate

In triangle \(ABC\) and its dilation \(A'B'C'\), side \(CA\) corresponds to side \(C'A'\). The length of \(CA = 50\), and the scale factor \(k=\frac{1}{2}\).
So, \(C'A'=CA\times k\)
Substitute \(CA = 50\) and \(k=\frac{1}{2}\) into the formula: \(C'A'=50\times\frac{1}{2}\)
\(C'A' = 25\)

Answer:

\(25\)