Select the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 13 , centered at the origin where the endpoints are A(−6,3) and B(−12,9).
a. A′(−18,9) and B′(−36,27)
b. A′(−2,1) and B′(−4,3)
c. A′(−2,1) and B′(−12,9)
d. A′(−6,3) and B′(−4,3)
The formula for dilation is:
x' = x * scale factor
y' = y * scale factor
Applying this formula to the coordinates of point A:
x' = -6 * 13 = -78
y' = 3 * 13 = 39
The coordinates of A' are (-78,39).
Applying the same formula to the coordinates of point B:
x' = -12 * 13 = -156
y' = 9 * 13 = 117
The coordinates of B' are (-156,117).
The correct option is a. A'(-78,39) and B'(-156,117).