Question

based on the image, the scale factor used to map p to p is:

Explanation:

Step1: Find coordinates of \(P\) and \(P'\)

Assume \(P(-6,9)\) and \(P'(-4,6)\) (by visual inspection of the graph).

Step2: Use scale - factor formula

The scale factor \(k\) for a dilation centered at the origin \((0,0)\) is given by \(k=\frac{x_{P'}}{x_{P}}=\frac{y_{P'}}{y_{P}}\).
Using \(x\) - coordinates: \(k = \frac{-4}{-6}=\frac{2}{3}\).
Using \(y\) - coordinates: \(k=\frac{6}{9}=\frac{2}{3}\).

Answer:

\(\frac{2}{3}\)