IF (-6, 4) is the endpoint of a line segment, and (-2, -1) is its midpoint, find the other endpoint. A) (2,-6) B) (-14, 14) 9 (-16, 12) D) (2,9)

Question

asked Jul 9, 2021 206k views

1 Answer

Sazzad · Answer 1 · 2021-07-14T01:00:32+0000

A midpoint has coordinates of
(-2, -1) we will call them
(x_m, y_m) .

The coordinates of a midpoint are constructed from coordinates of enpoints
(x_1,y_1),(x_2,y_2) , namely as a divided sum.

$x_m=(x_1+x_2)/(2)\implies x_1=2x_m-x_2 \\y_m=(y_1+y_2)/(2)\implies y_1=2y_m-y_2$

Now insert the numbers.

$x_1=2(-2)-(-6)=2 \\y_1=2(-1)-4=-6$

The result is an endpoint at
(2,-6) .