Question

the points c and c are depicted on the graph below. the point c is obtained by dilating c about the origin. what is the scale factor of this dilation?

Explanation:

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

From the graph, \(C=(-1,2)\) and \(C'=(-5,10)\).

Step2: Calculate scale factor

For dilation about the origin \((x,y)\to(kx,ky)\).
For \(x -\) coordinates: \(-5 = k\times(-1)\), so \(k=\frac{-5}{-1}=5\).
For \(y -\) coordinates: \(10 = k\times2\), so \(k=\frac{10}{2}=5\).

Answer:

\(5\)