Question

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)

Answer 1

To find the coordinates of A' and B' after dilation with a scale factor of 2, we can first find the distance between the origin and points A and B.

Distance from the origin to point A = √(x^2 + y^2) = √(3^2 + 7^2) = √(9 + 49) = √58
Distance from the origin to point B = √(x^2 + y^2) = √(4^2 + 9^2) = √(16 + 81) = √97

After dilation with a scale factor of 2, the distances from the origin to points A' and B' will be twice their original distances.

Distance from the origin to point A' = √58 * 2 = √116
Distance from the origin to point B' = √97 * 2 = √194

Since the dilation is centered at the origin, the coordinates of A' and B' will lie on the same line as A and B, but will be twice as far from the origin.

The coordinates of A' will be (2*3, 2*7) = (6, 14)
The coordinates of B' will be (2*4, 2*9) = (8, 18)

Therefore, A' has coordinates (6, 14) and B' has coordinates (8, 18).