Select the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 1/3 , centered at the origin where the endpoints are A(−6,3) and B(−12,9) .
To find the coordinates A' and B' after dilation, we need to multiply the coordinates of A and B by the scale factor of 1/3.
For point A(−6,3):
The x-coordinate of A' = (x-coordinate of A) * (scale factor) = (-6) * (1/3) = -2
The y-coordinate of A' = (y-coordinate of A) * (scale factor) = 3 * (1/3) = 1
Therefore, A' = (-2, 1).
For point B(−12,9):
The x-coordinate of B' = (x-coordinate of B) * (scale factor) = (-12) * (1/3) = -4
The y-coordinate of B' = (y-coordinate of B) * (scale factor) = 9 * (1/3) = 3
Therefore, B' = (-4, 3).
Thus, the coordinates A' are (-2,1) and B' are (-4,3).