Question

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

Explanation:

Step1: Recall the property of dilation

When a figure is dilated, the length of each side of the new figure (image) is equal to the length of the corresponding side of the original figure (pre - image) multiplied by the scale factor.

Step2: Identify the corresponding side and calculate

The side \(KI\) in \(\triangle IJK\) corresponds to the side \(K'I'\) in \(\triangle I'J'K'\). The length of \(KI = 60\), and the scale factor \(s=\frac{1}{2}\).
Using the formula \(l_{image}=l_{pre - image}\times s\), we substitute \(l_{pre - image}=60\) and \(s = \frac{1}{2}\).
So, \(K'I'=60\times\frac{1}{2}\)

$$K'I'=\frac{60}{2}=30$$

Answer:

\(30\)