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: Use 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.

For side \(KI\) in \(\triangle IJK\) with length \(s = 60\) and scale factor \(k=\frac{1}{2}\).

Step2: Calculate the length of \(K'I'\)

Substitute \(s = 60\) and \(k=\frac{1}{2}\) into the formula \(s'=s\times k\).

\(K'I'=60\times\frac{1}{2}\)

\(K'I' = 30\)

Answer:

\(30\)