Find the dilation of 0.5 with center (0, 0) for the following points if A (−6, 9) B (−9, 6)
To find the dilation of a point, you first need to determine the scale factor. The scale factor is the ratio of the distance between the original point and the center of dilation to the distance between the dilated point and the center of dilation.
For point A (-6, 9):
Distance between the original point and the center of dilation = sqrt((-6 - 0)^2 + (9 - 0)^2) = 10.81
Distance between the dilated point and the center of dilation = sqrt((0.5(-6) - 0)^2 + (0.5(9) - 0)^2) = sqrt((-3)^2 + (4.5)^2) = 5.35
Scale factor = Distance between the dilated point and the center of dilation / Distance between the original point and the center of dilation = 5.35 / 10.81 = 0.4949
So, the dilation of point A is 0.4949 with center (0, 0).
For point B (-9, 6):
Distance between the original point and the center of dilation = sqrt((-9 - 0)^2 + (6 - 0)^2) = 10.82
Distance between the dilated point and the center of dilation = sqrt((0.5(-9) - 0)^2 + (0.5(6) - 0)^2) = sqrt((-4.5)^2 + (3)^2) = 5.35
Scale factor = Distance between the dilated point and the center of dilation / Distance between the original point and the center of dilation = 5.35 / 10.82 = 0.4947
So, the dilation of point B is 0.4947 with center (0, 0).