Question

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

Explanation:

Step1: Apply dilation formula

For a point \((x,y)\) dilated by a scale factor \(k\) centered at the origin, the image is \((kx,ky)\). Here \(x = 12\), \(y=- 12\), \(k=\frac{1}{4}\).

Step2: Calculate \(x\)-coordinate of the image

\(kx=\frac{1}{4}\times12 = 3\)

Step3: Calculate \(y\)-coordinate of the image

\(ky=\frac{1}{4}\times(-12)=-3\)

Answer:

\((3,-3)\)