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

The scale factor of dilation can be found by comparing the lengths of corresponding sides.

Let's compare the length of a side from the original quadrilateral to the corresponding side in the new quadrilateral:
Original Quadrilateral:
Side 1: Length = Distance between (4,4) and (6,6) = √((6-4)^2+(6-4)^2) = √8 = 2√2
New Quadrilateral:
Side 1': Length = Distance between (3,3) and (4.5,4.5) = √((4.5-3)^2+(4.5-3)^2) = √2.5

The scale factor of dilation can be found by dividing the length of Side 1' by the length of Side 1:
Scale factor = Side 1' / Side 1 = (√2.5) / (2√2) = (1/2) * (√2.5/√2) = (1/2) * (√(2.5/2)) = (1/2) * (√(5/4)) = (1/2) * (√5/√4) = (1/2) * (√5/2) = √5/4

Therefore, the scale factor of dilation is √5/4.