The coordinates of midpoint M and endpoint A of a segment are M(-1, 2) and A(3, -5). Find the coordinates of the other endpoint.

Answer 1

Here's a picture:

To go from A to M in the x-direction, we need to subtract 4 (3 - 4 = -1) so, let's subtract 4 again to get to the other endpoint. -1 - 4 = -5. The x-coordinate of the other endpoint (I called it B) is -5.

To go from A to M in the y-direction, we need to add 7 (-5 + 7 = 2) so, let's add 7 again to get to the other endpoint. 2 + 7 = 9. The y-coordinate of the other endpoint is 9. So the other endpoint (point B) is at (-5, 9).

You can also do this using the midpoint formula x_m = (x₁ + x₂)/2 and y_m = (y₁ + y₂)/2 where the coordinates of the endpoints are (x₁, y₁) and (x₂, y₂) and the coordinates of the midpoint are (x_m, y_m). Then for the x direction:

-1 = (3 + x₂)/2

-2 = (3 + x₂)

x₂ = -5

And for the y-direction:

2 = (-5 + y₂)/2

4 = (-5 + y₂)

y₂ = 9

(x₂, y₂) = (-5, 9)