select the coordinates A' and B' after dilation of the line segment with 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 of the line segment AB with a scale factor of 1/3, centered at the origin, we can use the formula for dilation:
D(x, y) = (kx, ky)
Where (x, y) are the original coordinates, and (kx, ky) are the new coordinates after dilation with a scale factor of k.
For point A (-6, 3):
A' = (k(-6), k(3))
A' = (-6/3, 3/3)
A' = (-2, 1)
For point B (-12, 9):
B' = (k(-12), k(9))
B' = (-12/3, 9/3)
B' = (-4, 3)
Therefore, the coordinates A' and B' after dilation of the line segment AB with a scale factor of 1/3, centered at the origin, are A'(-2, 1) and B'(-4, 3).