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 points

For each vertex \(X\) (\(X = A,B,C\)), move along the line \(PX\) such that the distance from \(P\) to the image point \(X'\) is \(\frac{1}{3}\) of the distance from \(P\) to \(X\). For example, if we consider a vector \(\overrightarrow{PX}\), then \(\overrightarrow{PX'}=\frac{1}{3}\overrightarrow{PX}\).

Step3: Connect the image points

Once the image points \(A'\), \(B'\), and \(C'\) are located, connect them to form the dilated triangle \(\triangle A'B'C'\).

Answer:

The dilated triangle \(\triangle A'B'C'\) is formed by following the above - mentioned steps of dilation with center \(P\) and scale factor \(\frac{1}{3}\).