Question

The midpoint of a sègment is (6,-4) and one endpoint is (13,-2). Find the coordinates of the other endpoint.

Answer 1

Answer:

(- 1, - 6 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( $\frac{x_{1}+x_{2} }{2}$ , $\frac{y_{1}+y_{2} }{2}$ ) ← midpoint formula

Use this formula on the endpoints and equate to the coordinates of the midpoint.

let the other endpoint = (x, y) , then

$\frac{13+x}{2}$ = 6 ( multiply both sides by 2 )

13 + x = 12 ( subtract 13 from both sides )

x = - 1

$\frac{-2+y}{2}$ = - 4 ( multiply both sides by 2 )

- 2 + y = - 8 ( add 2 to both sides )

y = - 6

The coordinates of the other endpoint are (- 1, - 6 )

Answer 2

let other one be (x,y)

We know midpoint formula

$\boxed{\sf (x,y)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}$

$\\ \sf\longmapsto (6,-4)=\left(\dfrac{13+x}{2},\dfrac{-2+y}{2}\right)$

$\\ \sf\longmapsto \dfrac{13+x}{2}=6$

$\\ \sf\longmapsto 13+x=12$

$\\ \sf\longmapsto x=12-13$

$\\ \sf\longmapsto x=-1$

And

$\\ \sf\longmapsto \dfrac{-2+y}{2}=-4$

$\\ \sf\longmapsto -2+y=-8$

$\\ \sf\longmapsto y=-8+2$

$\\ \sf\longmapsto y=-6$