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’ (3/2 , 7/2) and B’ (2 , 9/2)
b. A’ (6,14) and B’ (8,18)
c. A’ (-6,3) and B’ (8,18)
d. A’ (6,14) and B’ (-4,3)
To find the coordinates A' and B' after dilation, we need to multiply the coordinates of A and B by the scale factor of 2.
For point A:
x-coordinate of A' = 2 * x-coordinate of A = 2 * 3 = 6
y-coordinate of A' = 2 * y-coordinate of A = 2 * 7 = 14
For point B:
x-coordinate of B' = 2 * x-coordinate of B = 2 * 4 = 8
y-coordinate of B' = 2 * y-coordinate of B = 2 * 9 = 18
Therefore, the coordinates of A' are (6, 14) and the coordinates of B' are (8, 18).
The correct answer is:
d. A’ (6,14) and B’ (-4,3)