Question

ΔRST is dilated about the origin, O, to create ΔR'S'T'. Point R is located at (3, 9), and point R' is located at (1.2, 3.6). Which scale factor was used to perform the dilation?

Answer 1

What you're doing here is multiplying all the sides of the triangle by a certain factor to produce a similar triangle (one with the same ratios between side lengths but different side lengths). When you scale a triangle in this way, the vertices (corners) of the triangle scale by the same factor. Therefore, by comparing the new coordinates for the vertex given to the original coordinates, you can figure out the scale factor:

1.2/3 = 0.4
3.6/9 = 0.4

The scale factor is 0.4.