Question

Rectangle ABCD has verticies A(1, 2) B(4, 2) C(1, -2) and D(4, -2). A dialation with a scale factor of 6 and centered at the origin is applied to the rectangle. Which vertex in the dilated image has coordinates of (24, 12)

A’
B’
C’
D’

Answer 1

B’

Explanation:

You want to know the vertex that has coordinates (24, 12) after dilation by a factor of 6 about the origin.

Dilation

When the center of dilation is the origin, the scale factor multiplies each coordinate value. Then the coordinates of the original point whose dilated location is (24, 12) is ...

6(x, y) = (24, 12)

(x, y) = (24, 12)/6 = (24/6, 12/6) = (4, 2) . . . . . . matches point B

The image point is B'.