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)

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 formulas:

For A':

x-coordinate of A' = (x-coordinate of A - x-coordinate of center) * scale factor + x-coordinate of center
y-coordinate of A' = (y-coordinate of A - y-coordinate of center) * scale factor + y-coordinate of center

For B':

x-coordinate of B' = (x-coordinate of B - x-coordinate of center) * scale factor + x-coordinate of center
y-coordinate of B' = (y-coordinate of B - y-coordinate of center) * scale factor + y-coordinate of center

Let's substitute the given values:

Center = (0, 0)
Scale factor = 2
A = (3, 7)
B = (4, 9)

For A':

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

Therefore, A' = (6, 14).

For B':

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

Therefore, B' = (8, 18).

So, the coordinates for A' and B' after dilation with a scale factor of 2 centered at the origin are A' (6, 14) and B' (8, 18).