Question

what is the image of $(12, -8)$ after a dilation by a scale factor of $\frac{1}{4}$ centered at the origin?

Explanation:

Step1: Multiply the x - coordinate by the scale factor

For the point \((12,-8)\), the x - coordinate is \(x = 12\). After dilation with a scale factor \(k=\frac{1}{4}\), the new x - coordinate \(x'=12\times\frac{1}{4}\).
Using the formula \(x' = kx\), we have \(x'=\frac{12}{4}=3\).

Step2: Multiply the y - coordinate by the scale factor

The y - coordinate of the point \((12,-8)\) is \(y=-8\). After dilation with a scale factor \(k = \frac{1}{4}\), the new y - coordinate \(y'=-8\times\frac{1}{4}\).
Using the formula \(y'=ky\), we get \(y'=\frac{-8}{4}=-2\).

Answer:

$(3, - 2)$