Question

triangle ijk is dilated by a scale factor of \\( \frac { 1 } { 2 } \\) to form triangle \\( i ^ { prime } j ^ { prime } k ^ { prime } \\). what is the measure of side \\( k ^ { prime } i ^ { prime } \\)?

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. The formula is \(l_{\text{image}}=l_{\text{pre - image}}\times\text{scale factor}\).

Step2: Identify the corresponding side and calculate

In triangle \(IJK\) and its dilated image \(I'J'K'\), side \(KI\) corresponds to side \(K'I'\). Given that the scale factor is \(\frac{1}{2}\) and the length of \(KI = 60\).
Using the formula \(l_{K'I'}=l_{KI}\times\frac{1}{2}\)
Substitute \(l_{KI} = 60\) into the formula: \(l_{K'I'}=60\times\frac{1}{2}\)
\(l_{K'I'}=30\)

Answer:

\(30\)