Question

what is the image of $(2, -4)$ after a dilation by a scale factor of 2 centered at the origin?

Explanation:

Step1: Recall the dilation formula

For a point \((x,y)\) dilated by a scale factor \(k\) centered at the origin, the formula is \((kx,ky)\).

Step2: Substitute the values

Here \(x = 2\), \(y=-4\) and \(k = 2\).
So, \(kx=2\times2 = 4\) and \(ky=2\times(-4)=-8\).

Answer:

\((4,-8)\)