select the coordinates A' and B' after 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' (8, 18)
b A' (-6, 3) and B' (8, 18)
c A' (6, 14) and B' (-4, 3)
d A' (3/2, 7/2) and B' (2, 9/2)
To find the coordinates after dilation, we multiply both the x-coordinate and the y-coordinate of each point by the scale factor.
The scale factor is 2, so we multiply the x-coordinate of A(3, 7) by 2 to find the x-coordinate of A':
x-coordinate of A' = 3 * 2 = 6
We also multiply the y-coordinate of A(3, 7) by 2 to find the y-coordinate of A':
y-coordinate of A' = 7 * 2 = 14
Therefore, A' is (6, 14).
Similarly, we multiply the x-coordinate of B(4, 9) by 2 to find the x-coordinate of B':
x-coordinate of B' = 4 * 2 = 8
We also multiply the y-coordinate of B(4, 9) by 2 to find the y-coordinate of B':
y-coordinate of B' = 9 * 2 = 18
Therefore, B' is (8, 18).
The correct answer is a) A' (6, 14) and B' (8, 18).