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: Identify the original side length

The original side length \( CA = 50\).

Step2: Apply the dilation formula

When a figure is dilated by a scale factor \(k\), the length of a side of the new figure \(s'\) is given by \(s'=k\times s\), where \(s\) is the length of the corresponding side of the original figure. Here \(k = \frac{1}{2}\) and \(s = CA = 50\). So \(C'A'=\frac{1}{2}\times50\).

Step3: Calculate the new side length

\(C'A'=\frac{50}{2}=25\)

Answer:

\(25\)