Question

draw the image of \\( \triangle a b c \\) under a dilation whose center is \\( p \\) and scale factor is \\( \frac { 1 } { 3 } \\).

Explanation:

Step1: Connect each vertex of \(\triangle ABC\) to the center \(P\)

Draw lines \(PA\), \(PB\), and \(PC\).

Step2: Locate the image vertices

On each line \(PA\), \(PB\), \(PC\), find a point such that the distance from \(P\) to the new point is \(\frac{1}{3}\) of the distance from \(P\) to the original vertex. For example, if the distance from \(P\) to \(A\) is \(d_{PA}\), then the distance from \(P\) to \(A'\) (the image of \(A\)) is \(\frac{1}{3}d_{PA}\). Do the same for \(B\) (to get \(B'\)) and \(C\) (to get \(C'\)).

Step3: Connect the image vertices

Connect \(A'\), \(B'\), and \(C'\) to form the dilated triangle \(\triangle A'B'C'\).

Answer:

Follow the above three - step drawing process to obtain the image of \(\triangle ABC\) under the given dilation.