A quadrilateral has the following vertices: (4,4), (6,6), (8,4), (6,2). After dilation, the new quadrilateral has the following vertices: (3,3), (4.5,4.5), (6,3), (4.5,1.5).(1 point)

Answer 1

To find the scale factor of the dilation, we can compare the distance between corresponding vertices of the original and new quadrilateral.

The distance between (4,4) and (6,6) is equal to √((6-4)^2 + (6-4)^2) = √8.
Similarly, the distance between (4.5,4.5) and (6,6) is equal to √((6-4.5)^2 + (6-4.5)^2) = √4.5.

Therefore, the scale factor of the dilation is √4.5/√8 = √0.5625 = 0.75.

To find the new coordinates of the original quadrilateral after dilation, we multiply the coordinates of each vertex by the scale factor:

(4,4) -> (4 * 0.75, 4 * 0.75) = (3,3)
(6,6) -> (6 * 0.75, 6 * 0.75) = (4.5,4.5)
(8,4) -> (8 * 0.75, 4 * 0.75) = (6,3)
(6,2) -> (6 * 0.75, 2 * 0.75) = (4.5,1.5)

Therefore, the new quadrilateral has the vertices (3,3), (4.5,4.5), (6,3), and (4.5,1.5).