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) .(1 point)
Responses
A′(−6,3) and B′(8,18)
A′(3/2,7/2) and B′(2,9/2)
A′(6,14) and B′(8,18)
A′(6,14) and B′(−4,3)
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 can use the formula:
A'(x', y') = (2(x - 0), 2(y - 0))
B'(x', y') = (2(x - 0), 2(y - 0))
Let's substitute the values for A(3,7) and B(4,9) into the formula:
A' = (2(3 - 0), 2(7 - 0)) = (6, 14)
B' = (2(4 - 0), 2(9 - 0)) = (8, 18)
Therefore, the correct answer is A′(6,14) and B′(8,18).