Question

Explaining How to Find an Image
Segment AB has endpoints A(–4, 6) and B(1, 4). After a dilation, centered at the origin, the image of A is (–6, 9). Without measuring the distance, explain how you could find the image of B.

Answer 1

A dilation centered at the origin multiplies every coordinate by the same scale factor k. From A(−4,6) → A'(−6,9) we get k = (−6)/(−4) = 3/2 (or from 9/6 = 3/2). Apply k to B(1,4):

B' = (1·3/2, 4·3/2) = (3/2, 6).

So the image of B is (3/2, 6).