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 meas

Question

Andrew [12]

3 years ago

10

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 meas

uring the distance, explain how you could find the image of B

Mathematics

2 answers:

Ksivusya [100] · Answer 1 · 2022-02-16T08:51:14+03:00

Ksivusya [100]3 years ago

4 0

With A and its image one can get the dilation factor;
That is dilation scale factor = -6/-4 or 9/6 = 3/2
Therefore, to get the image of B we multiply the coordinates of B by the dilation factor;
(1,4) 3/2 = (1.5, 6)
Thus the image of B = (1.5,6)

-BARSIC- [3] · Answer 2 · 2022-02-16T10:15:35+03:00

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: