Question

Square ABCD is dilated by a scale factor of 2 with the center of dilation at the origin to form square ABCD . What are the coordinates of vertex B. A(2,7) C(8,1) D(2,1)

Answer 1

B'(16,14)

Explanation:

In square ABCD, A(2,7) C(8,1) D(2,1). First, find the coordinates of the vertex B. From the attached diagram you can see that CD=6 units and is parallel to the x-axis, AD=6 units and is parallel to the y-axis. So, B(8,7).

The origin O is the center of dilation, 2 is the scale factor. The rule of the dilation is

(x,y)→(2x,2y)

Thus,

B(8,7)→B'(16,14) (see attached figure).