select the coordinates A' and B' after the dilation of the line segment AB with a scale factor of 2 centered at the origin where the endpoints are A (3,7) and B (4,9)

A. A' (6,14) and B' (-4,3)
B.A'(3/2,7/2) and B' (2,9/2)
C.A' (6,14) and B'(8,18)
D.A' (-6,3) and B'(8,18)

1 answer

To find the coordinates A' and B' after dilation of the line segment AB with a scale factor of 2 centered at the origin, we need to double the distance between each point and the origin.

Given A (3,7) and B (4,9):

A' = (2 * 3, 2 * 7) = (6, 14)
B' = (2 * 4, 2 * 9) = (8, 18)

Therefore, the correct answer is:
C. A' (6,14) and B' (8,18)