Question

What is the image of (9,3) after a dilation by a scale factor of 3 centered at the
origin?

Answer 1

Answer:  (27, 9)

Multiply the original coordinates by the scale factor 3 to get this answer

9*3 = 27

3*3 = 9

This only works if the center of dilation is the origin.

The general rule is $(x,y) \to (kx, ky)$ where k is the scale factor.