select the coordinates A' and B' after dilation of the line segment AB with a scale factor of 2, centered at the origin where endpoints are A(3,7) and B(4,9).
1. A'(6,14) and B' (-4,3)
2. A'(-6,3) and B' (8, 18)
3. A'(3/2,7/2) and (2,9/2)
4. A'(6,14) and B' (8,18)
The correct answer is 1. A'(6,14) and B' (-4,3).
To find the coordinates A' and B' after dilation with a scale factor of 2 and centered at the origin, we need to multiply the x and y coordinates of A and B by the scale factor.
For A(3,7):
x-coordinate of A' = 3 * 2 = 6
y-coordinate of A' = 7 * 2 = 14
For B(4,9):
x-coordinate of B' = 4 * 2 = 8
y-coordinate of B' = 9 * 2 = 18
Therefore, A' has coordinates (6,14) and B' has coordinates (-4,3).