Question

Point A is a vertex of a polygon. Point A' is the image of A after the dilation. Find the scale factor of the dilation. The point of dilation is the origin.

A (-2, -3) and A'( -10, -15)

k (scale factor) =

Answer 1

The scale factor of a dilation, denoted as k, is the ratio of the length of a line segment in the image to the corresponding line segment in the original figure.

Given that the point of dilation is the origin, we can calculate the scale factor k by dividing the coordinates of the image point A'(-10, -15) by the corresponding coordinates of the original point A(-2, -3).

So, for the x-coordinates: k = -10 / -2 = 5 And for the y-coordinates: k = -15 / -3 = 5

Therefore, the scale factor k of the dilation is 5.