Question

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Polygon ABCD is reflected and dilated to give polygon PQRS. The coordinates of the preimage are (2, 2), (6, 8), (12, 8), and (16, 2). The coordinates of the image are (11, 15), (9, 12), (6, 12), and (4, 15). What is the scale factor of the dilation?

Answer 1

Explanation:

It is given the A B C D is polygon which is reflected and dilated, then we get P Q R S.

The vertices A B C D are (2,2),(6,8),(12,8), and (16,2) respectively. the vertices of image P,Q,R,S are (11,15),(9,12),(6,12) and (4,15) respectively

The reflection affects the coordinates but does not affect the length of the sides.

But when we talk about dilation it affects the length of he sides according to the scale factor or constant factor or a constant factor.

if a line segment is dilated by scale factor K times length of A,B then length of A,B is K times the length of A,B
|A,B|=Kx|A,B|

so we have to find any side length of preimage and the side length of that side in image. It means that we would have to find A,B and P,Q.

use the distance formula to find the side length

Answer 2

if you do the correct math your answer will be K=0.5