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

[AI-generated answer — Bot GPT 3.5]

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

A' = (scale factor * (Ax - center_x) + center_x, scale factor * (Ay - center_y) + center_y)
B' = (scale factor * (Bx - center_x) + center_x, scale factor * (By - center_y) + center_y)

In this case, the center is the origin (0, 0), and the scale factor is 2. Substituting the given values into the formula:

For A':

A'x = (2 * (3 - 0) + 0) = 6
A'y = (2 * (7 - 0) + 0) = 14

So A' = (6, 14)

Similarly, for B':

B'x = (2 * (4 - 0) + 0) = 8
B'y = (2 * (9 - 0) + 0) = 18

So B' = (8, 18)

Therefore, the coordinates A' and B' after dilation are A' = (6, 14) and B' = (8, 18).