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) .

Answer 1

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

The length between (4,4) and (6,6) in the original quadrilateral is:
√[(6 - 4)^2 + (6 - 4)^2] = √[2^2 + 2^2] = √8

The length between (3,3) and (4.5,4.5) in the new quadrilateral is:
√[(4.5 - 3)^2 + (4.5 - 3)^2] = √[1.5^2 + 1.5^2] = √4.5

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

To find the coordinates of the new quadrilateral, we multiply the coordinates of the original quadrilateral by the scale factor.

The coordinates of the new quadrilateral are:
(4,4) * 0.75 = (3,3)
(6,6) * 0.75 = (4.5,4.5)
(8,4) * 0.75 = (6,3)
(6,2) * 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) after dilation.

Answer 2

the answer is a number that is not in "( )"