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 A' and B' after dilation of the line segment AB with a scale factor of 2 centered at the origin, we need to first calculate the coordinates of the midpoint of AB, which will serve as the center of dilation.

Midpoint of AB:
x-coordinate of midpoint = (x1 + x2) / 2 = (3 + 4) / 2 = 3.5
y-coordinate of midpoint = (y1 + y2) / 2 = (7 + 9) / 2 = 8

Therefore, the midpoint of AB is (3.5, 8).

Now, to find the coordinates A' and B' after dilation with scale factor of 2, we will use the formula for dilation centered at the origin:

A' = 2(3.5 - 0) + 0 = 7
2(8 - 0) + 0 = 16
Therefore, A' = (7, 16).

Similarly, for B':
B' = 2(4 - 0) + 0 = 8
2(9 - 0) + 0 = 18
Therefore, B' = (8, 18).

So, after dilation of the line segment AB with a scale factor of 2 centered at the origin, the coordinates A' and B' are A' (7, 16) and B' (8, 18), respectively.