Question

1. ( p(12,-3) ) is the image of ( p ) after a dilation centered at the origin with a scale factor of 3. what are the coordinates of ( p )? 13. identify the scale factor used to graph the image below.

Explanation:

Step1: Recall the dilation formula

If a point \(P(x,y)\) is dilated about the origin with a scale factor \(k\) to get \(P'(x',y')\), then \(x' = kx\) and \(y'=ky\). Here \(k = 3\), \(x'=12\), \(y'=- 3\).

Step2: Solve for \(x\) and \(y\)

For the \(x\) - coordinate:
Since \(x'=kx\), then \(x=\frac{x'}{k}\). Substituting \(x' = 12\) and \(k = 3\), we have \(x=\frac{12}{3}=4\).
For the \(y\) - coordinate:
Since \(y'=ky\), then \(y=\frac{y'}{k}\). Substituting \(y'=-3\) and \(k = 3\), we have \(y=\frac{-3}{3}=-1\).

Answer:

The coordinates of \(P\) are \((4,-1)\)