# How do you find the coordinates of the other endpoint of a segment with the given midpoint is (5,-11) and the other end point is (3,5)?

Aug 16, 2017

Other end point: color(red)(""(7,-27))

#### Explanation:

If $\left({x}_{m} , {y}_{m}\right)$ is the mid-point between $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$
then
$\textcolor{w h i t e}{\text{XXX")(x_2-x_m)=(x_m-x_1)color(white)("xxx")rarr color(white)("xxx}} {x}_{2} = {x}_{m} + \left({x}_{m} - {x}_{1}\right)$
and
$\textcolor{w h i t e}{\text{XXX")(y_2-y_m)=(y_m-y_1))color(white)("xxx")rarr color(white)("xxx}} {y}_{2} = {y}_{m} + \left({x}_{m} - {y}_{1}\right)$

In this case
$\textcolor{w h i t e}{\text{XXX")(x_m-x_1)=5-3=2color(white)("xxxxxxxx")rarr color(white)("xxx}} {x}_{2} = 5 + 2 = 7$
and
$\textcolor{w h i t e}{\text{XXX")(y_m-y_1)=-11-5=-16color(white)("xx")rarr color(white)("xxx}} {y}_{2} = - 11 + \left(- 16\right) = - 27$