Question

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

If the image is centered at the origin you can divide the terms of the image from the preimage to find the scale or ratio at which it was dilated. In this case, you will use the points of A because the point b does not matter in this case.

$\frac{-6}{-4} = 1.5$  and $\frac{9}{6} = 1.5$ so the image is dilated by a scale of 1.5

now that we know the scale we multiply the points of B by the scale to get the image.    1*1.5 = 1.5  and 4*1.5 = 6 so the image for B is (1.5, 6) 

Answer 2

Answer:

To find the image of B, first find the scale factor for the dilation. The scale factor should be greater than 1 because the image of A is farther from the origin than A. Divide the coordinates of the image of A by the coordinates of A: –6/–4 = 3/2 and 9/6 = 3/2, so the scale factor is 3/2. Now, apply the dilation to B by multiplying the coordinates by 3/2 to get ((3/2)(1), (3/2)(4)), or (3/2, 6).