in each of the following graphs, the two given polygons are similar. write precisely a single dilation (coordinated of center an

Question

2 years ago

13

d coefficient) by which the image (labled with primed letters) was obtained.

1 answer:

Sergeeva-Olga [200] · Answer 1 · 2023-03-12T08:13:24+03:00

The single dilation of the shape is a dilation by a scale factor of 1.5 with center R

<h3>How to determine the dilation rule?</h3>

From the graph, we have the center of dilation to be point R.

This is so because R = R'

Also, we have:

R = (-1, -4)

S = (2, 0)

S' = (3.5, 2)

Calculate the distance RS and RS' using

$d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2$

This gives

$RS = \sqrt{(0 + 4)^2 + (2+ 1)^2} = 5$

$RS' = \sqrt{(2 + 4)^2 + (3.5+ 1)^2} = 7.5$

Divide RS' by RS to determine the scale factor (k)

k = 7.5/5

k = 1.5

Hence, the single dilation of the shape is a dilation by a scale factor of 1.5 across point R