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).
Responses:
A′(−6,3) and B′(−4,3)
A′(−2,1) and B′(−12,9)
A′(−2,1) and B′(−4,3)
A′(−18,9) and B′(−36,27)
To find the coordinates A' and B' after dilation, we can use the formula:
A' = (scale factor) * (xA, yA)
B' = (scale factor) * (xB, yB)
Given that the scale factor is 13 and the endpoints are A(-6, 3) and B(-12, 9), we can calculate the coordinates A' and B' as follows:
A' = 13 * (-6, 3) = (-78, 39)
B' = 13 * (-12, 9) = (-156, 117)
Therefore, the correct option is:
A′(-78,39) and B′(-156,117)