Parallelogram W'X'Y'Z' is the image of parallelogram WXYZ after a dilation. WXYZ has coordinates W(–8,4), X(–4,8), Y(8,4), and Z(4,0). W'X'Y'Z' has coordinates W'(–6,3), X'(–3,6), Y'(6,3), and Z'(3,0).What are the scale factor and center of the dilation that maps WXYZ to W'X'Y'Z'?The scale factor is 34, and the center is the origin.The scale factor is 34, and the center is point W.The scale factor is 43, and the center is the origin.The scale factor is 43, and the center is point W.Submit

The scale factor of a dilation is determined by the ratio of the lengths of corresponding sides in the image and the pre-image. In this case, we can use the distance formula to calculate the lengths of corresponding sides in WXYZ and W'X'Y'Z'.

Let's calculate the length of WZ in WXYZ:

WZ = sqrt[(4-0)^2 + (-8-4)^2] = sqrt[16 + 144] = sqrt[160] = 4sqrt[10]

Now, let's calculate the length of W'Z' in W'X'Y'Z':

W'Z' = sqrt[(3-0)^2 + (-6-3)^2] = sqrt[9 + 81] = sqrt[90] = 3sqrt[10]

The scale factor is then W'Z'/WZ = (3sqrt[10])/(4sqrt[10]) = 3/4.

Therefore, the scale factor is 3/4.

The center of dilation is the only point that remains fixed after the dilation. In this case, since all points have been moved, the center of dilation is not one of the vertices of the parallelogram. However, since the coordinates of the vertices in W'X'Y'Z' are 3/4 of the coordinates of the corresponding vertices in WXYZ, the center of dilation is the origin (0,0).

Therefore, the scale factor is 3/4, and the center of dilation is the origin.