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?
0.25
0.33
0.5
0.75
0.25 this website is a joke the answer was wrong
the answer i don't know what it is?
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To find the scale factor of the dilation, we need to compare the corresponding side lengths of the preimage and the image.
For example, let's compare the length of AB in the preimage to the length of PQ in the image. The length of AB is the distance between the points (2, 2) and (6, 8). Using the distance formula, the length of AB is:
√((6 - 2)^2 + (8 - 2)^2)
= √(4^2 + 6^2)
= √(16 + 36)
= √52
Similarly, the length of PQ is the distance between the points (11, 15) and (9, 12). Using the distance formula, the length of PQ is:
√((9 - 11)^2 + (12 - 15)^2)
= √((-2)^2 + (-3)^2)
= √(4 + 9)
= √13
The scale factor of the dilation is the ratio of the corresponding side lengths. So, the scale factor is:
√13 / √52
= (√13 / √(13*4))
= (√13 / (2 √13))
= 1 / 2
Therefore, the scale factor of the dilation is 1/2, or 0.5.