Question

what is the image of $(-8,0)$ after a dilation by a scale factor of $\frac{1}{4}$ centered at the origin?

Explanation:

Step1: Apply the dilation formula

For a point \((x,y)\) dilated by a scale factor \(k\) centered at the origin, the new point is \((kx,ky)\). Here \(x=-8\), \(y = 0\), and \(k=\frac{1}{4}\).

Step2: Calculate the new \(x\) - coordinate

\(kx=\frac{1}{4}\times(-8)=- 2\)

Step3: Calculate the new \(y\) - coordinate

\(ky=\frac{1}{4}\times0 = 0\)

Answer:

\((-2,0)\)