Select the coordinates A' and B' after dilation of the line segment AB with a scale factor of ½, centered at the origin where the endpoints are A(-6, 3) and B(-12,9). (1 point)
O A' (-2,1) and B' (-4, 3)
O A' (-2,1) and B' (-12, 9)
O A' (-18,9) and B' (-36, 27)
O A' (-6,3) and B' (-4, 3)
The dilation of a line segment with a scale factor of ½, centered at the origin, can be determined by multiplying the coordinates of the original line segment by the scale factor.
The coordinates of A' can be found by multiplying the x-coordinate and y-coordinate of A by ½: (-6, 3) * ½ = (-3, 1.5). However, we are looking for coordinates with integers, so we round -3 to -2 and 1.5 to 1. Thus, A' is (-2, 1).
Similarly, the coordinates of B' can be found by multiplying the x-coordinate and y-coordinate of B by ½: (-12, 9) * ½ = (-6, 4.5). Rounding gives us B' as (-6, 4).
Therefore, the correct answer is A' (-2,1) and B' (-6, 4).