Question

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)

Answer 1

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.

`</p><p>x_m=(x_1+x_2)/(2)\implies x_1=2x_m-x_2 \\</p><p>y_m=(y_1+y_2)/(2)\implies y_1=2y_m-y_2</p><p>`

Now insert the numbers.

`</p><p>x_1=2(-2)-(-6)=2 \\</p><p>y_1=2(-1)-4=-6</p><p>`

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