Question

A dilation has center (0, 0). Find the image of the point B (-2, 6) for the scale factor of 5.

Answer 1

Since the center of the dilation is (0,0) [the same as the origin of the coordinate system], simply multiply the coordinates for the point by the dilation factor: (-2*5, -2*6) = (-10, 30). [When the center of the dilation is not the origin, then use vector addition: add (sum) the vector from the center of the dilation to the origin and the vector from the origin to the point; multiply this sum vector by the dilation factor MINUS ONE; add this product vector to the vector from the origin to the point. This is like translating the origin of the coordinate system to the center of the dilation, performing the dilation, then translating the origin back to (0,0) (hence the minus one...).]

Answer 2

Oops, that second coordinate multiplied by the dilation factor should have been 6*5 [so -2*5,6*5)]; the answer given is right, though -- (-10, 30).