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

Answer:

see the explanation

Step-by-step explanation:

step 1

Find the scale factor of the dilation

Divide the x-coordinate or the y-coordinate of the image by the the x-coordinate or the y-coordinate of the pre-image

so

$\frac{-6}{-4}=1.5$

or

$\frac{9}{6}=1.5$

step 2

Multiply the coordinates of point B by the scale factor to obtain the image B'

B'(1.5*1,1.5*4)

B'(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).

Step-by-step explanation: its the sample response