A quadrilateral has the following vertices: (4,4)%0D%0A(%0D%0A4%0D%0A,%0D%0A4%0D%0A)%0D%0A , (6,6)%0D%0A(%0D%0A6%0D%0A,%0D%0A6%0D%0A)%0D%0A , (8,4)%0D%0A(%0D%0A8%0D%0A,%0D%0A4%0D%0A)%0D%0A , (6,2)%0D%0A(%0D%0A6%0D%0A,%0D%0A2%0D%0A)%0D%0A . After dilation, the new quadrilateral has the following vertices: (3,3)%0D%0A(%0D%0A3%0D%0A,%0D%0A3%0D%0A)%0D%0A , (4.5,4.5)%0D%0A(%0D%0A4.5%0D%0A,%0D%0A4.5%0D%0A)%0D%0A , (6,3)%0D%0A(%0D%0A6%0D%0A,%0D%0A3%0D%0A)%0D%0A , (4.5,1.5)%0D%0A(%0D%0A4.5%0D%0A,%0D%0A1.5%0D%0A)%0D%0A .
The dilation factor can be found by comparing the corresponding sides of the original quadrilateral and the new quadrilateral.
The side length from (4,4) to (6,6) in the original quadrilateral is √[(6-4)^2 + (6-4)^2] = √8.
The side length from (3,3) to (4.5,4.5) in the new quadrilateral is √[(4.5-3)^2 + (4.5-3)^2] = √2.5.
Therefore, the dilation factor is √2.5 / √8 ≈ 0.7906.
To find the coordinates of the new quadrilateral, we can multiply the x and y coordinates of each vertex of the original quadrilateral by the dilation factor.
The new coordinates are:
(4 * 0.7906, 4 * 0.7906) = (3.1624, 3.1624)
(6 * 0.7906, 6 * 0.7906) = (4.7436, 4.7436)
(8 * 0.7906, 4 * 0.7906) = (6.3248, 3.1624)
(6 * 0.7906, 2 * 0.7906) = (4.7436, 1.5812)
So, the new quadrilateral has the vertices: (3.1624, 3.1624), (4.7436, 4.7436), (6.3248, 3.1624), (4.7436, 1.5812).
what is the scale factor
The scale factor is the ratio of the corresponding side lengths of the new and original quadrilaterals.
In this case, we can calculate the scale factor by dividing the length of any side in the new quadrilateral by the length of the corresponding side in the original quadrilateral.
For example, let's consider the side from (4,4) to (6,6) in the original quadrilateral. The length is √[(6-4)^2 + (6-4)^2] = √8.
In the new quadrilateral, the corresponding side is from (3,3) to (4.5,4.5), with a length of √[(4.5-3)^2 + (4.5-3)^2] = √2.5.
The scale factor is then √2.5 / √8 ≈ 0.7906.
So, the scale factor is approximately 0.7906.