Answer:
The correct answer is: OA(3, -4.5), B(1.5, -1.5), C(-3, 1.5), D'(-3,-3).
To dilate a point using a scale factor of 4, we multiply each coordinate of the original point by 4.
Thus, the coordinates of A' are (-4 * 4, 6 * 4) = (-16, 24)
The coordinates of B' are (-2 * 4, 2 * 4) = (-8, 8)
The coordinates of C' are (4 * 4, -2 * 4) = (16, -8)
The coordinates of D' are (4 * 4, 4 * 4) = (16, 16)
To check our work, we can plot these points on a graph and compare with the original polygon:
Original Polygon:
A(-4, 6) B(-2, 2)
* *
\ /
\ /
\ /
\ /
\ /
* *
C(4,-2) D(4,4)
Dilated Polygon:
A'(-16, 24) B'(-8, 8)
* *
\ /
\ /
\ /
*
C'(16,-8) D'(16,16)
If we divide the coordinates of the dilated polygon by 4, we get the answer:
A'(-16/4, 24/4) = (-4, 6)
B'(-8/4, 8/4) = (-2, 2)
C'(16/4, -8/4) = (4, -2)
D'(16/4, 16/4) = (4, 4)
So the vertices of polygon A'B'C'D' are OA (3, -4.5), B(1.5, -1.5), C(-3, 1.5), and D'(-3,-3).