Select the coordinates A’ and B’ after dilation of the line, segment AB, with a scale factor of one third centered at the origin, where the end points 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 one third.
Coordinates of A:
x-coordinate of A’ = (x-coordinate of A) * scale factor
= (-6) * (1/3)
= -2
y-coordinate of A’ = (y-coordinate of A) * scale factor
= 3 * (1/3)
= 1
Therefore, the coordinates of A’ are (-2, 1).
Coordinates of B:
x-coordinate of B’ = (x-coordinate of B) * scale factor
= (-12) * (1/3)
= -4
y-coordinate of B’ = (y-coordinate of B) * scale factor
= 9 * (1/3)
= 3
Therefore, the coordinates of B’ are (-4, 3).
Hence, the coordinates A’ are (-2, 1) and B’ are (-4, 3).