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

Answer 1

To find the coordinates of A' and B' after dilation with a scale factor of 2, centered at the origin, we can use the following formula:

A' = (scale factor * x-coordinate of A, scale factor * y-coordinate of A)
B' = (scale factor * x-coordinate of B, scale factor * y-coordinate of B)

In this case, the scale factor is 2. Therefore, we have:

A' = (2 * 3, 2 * 7) = (6, 14)
B' = (2 * 4, 2 * 9) = (8, 18)

So, the correct answer is option 3: A'(6,14) and B'(8,18).