Line AB contains point A (2, -5) and point B (-3, -2). Find the coordinates of A' and B' after a dilation with a scale factor of 4 with a center point of dilation at the origin.
A. A's (8, -20) and B' (-3, -2)
B. A' (8, 20) and B' (12, 8)
C. A' (8, -20) and B' (-12, -8)
D. A' (2, -5) and B' (-12, -8)
To find the coordinates of A' and B' after a dilation with a scale factor of 4, we can multiply the x-coordinate and the y-coordinate of each point by 4. Note that the center point of dilation is the origin (0, 0).
For point A (2, -5), the coordinates of A' after dilation are (4*2, 4*(-5)) = (8, -20).
For point B (-3, -2), the coordinates of B' after dilation are (4*(-3), 4*(-2)) = (-12, -8).
Therefore, the correct answer is C. A' (8, -20) and B' (-12, -8).