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)

Question

A′(6,14) and B′(−4,3)
A′(3/2,7/2) and B′(2,9/2)
A′(−6,3) and B′(8,18)
A′(6,14) and B′(8,18)

Answer 1

To find the coordinates of the points A' and B' after dilation of points A(3,7) and B(4,9) with a scale factor of 2 centered at the origin, we will multiply the coordinates of each point by the scale factor.

1. For point A (3, 7): \[ A' = (3 \times 2, 7 \times 2) = (6, 14) \]

2. For point B (4, 9): \[ B' = (4 \times 2, 9 \times 2) = (8, 18) \]

Thus, the coordinates after dilation are:

• A'(6, 14)
• B'(8, 18)

So the correct choice is: A′(6,14) and B′(8,18).