DE is a line segment with endpoints D(-5,1) and E(3, 3). What are the coordinates of Dβ and Eβ, the image of DE under a dilation of magnitude 1.5 and a center of dilation at the point (-4,2)?
Accepted Solution
A:
First step is to calculate distance between point D and center of dilation: x= |-4-(-5)| =1Β y= |2-1| =1
Now we multiply this distance by the dilation factor x_distance = 1 * 1.5 = 1.5 y_distance = 1 * 1.5 = 1.5
Now we do same for point E: x= |-4-3| =7Β y= |2-3| =1
Now we multiply this distance by the dilation factor x_distance = 7 * 1.5 = 10.5 y_distance = 1 * 1.5 = 1.5
Now we need to find coordinates for points D' and E'. Point D': x = -4 - 1.5 = -5.5 y = 2 + 1.5 = 3.5 Point E': x= -4 + 10.5 = 6.5 y= 2 + 1.5 = 3.5