Question

1. p(-2,5) is the image of p after a dilation centered at the origin with a scale factor of 1/3. what are the coordinates of p?

Explanation:

Step1: Recall the dilation formula

If a point \(P(x,y)\) is dilated about the origin with a scale factor \(k\), the image \(P'(x',y')\) is given by \(x' = kx\) and \(y'=ky\). Here \(k=\frac{1}{3}\), \(x'=- 2\), \(y' = 5\).

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

Since \(x'=\frac{1}{3}x\), then \(x = 3x'\). Substituting \(x'=-2\), we get \(x=3\times(-2)=-6\).
Since \(y'=\frac{1}{3}y\), then \(y = 3y'\). Substituting \(y' = 5\), we get \(y=3\times5 = 15\).

Answer:

The coordinates of \(P\) are \((-6,15)\)