Question

what is the image of (-12, -4) after a dilation by a scale factor of \\(\frac{1}{4}\\) centered at the origin?

Explanation:

Step1: Recall dilation rule

To dilate a point \((x,y)\) centered at the origin with a scale factor \(k\), we multiply the coordinates by \(k\), so the new point is \((kx,ky)\).

Step2: Apply the rule

Given the point \((-12,-4)\) and scale factor \(k = \frac{1}{4}\), we calculate the new \(x\)-coordinate: \(-12\times\frac{1}{4}=-3\) and the new \(y\)-coordinate: \(-4\times\frac{1}{4}=-1\).

Answer:

\((-3, -1)\)