# How do you find the coordinates of the other endpoint of a segment with the given Endpoint: A(2,7) and midpoint: M(1,6)?

Feb 4, 2017

Other endpoint is $\left(0 , 5\right)$

#### Explanation:

The midpoint of a segment with endpoints as $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is $\left(\frac{{x}_{1} + {x}_{2}}{2} , \frac{{y}_{1} + {y}_{2}}{2}\right)$

Here we have been given one endpoint as $A \left(2 , 7\right)$ and let the other endpoint be $B \left(x , y\right)$. As their midpoint is $M \left(1 , 6\right)$, we must have

$\frac{x + 2}{2} = 1$ i.e. $x + 2 = 2$ or $x = 0$ and

$\frac{y + 7}{2} = 6$ i.e. $y + 7 = 12$ or $y = 5$

Hence, other endpoint is $\left(0 , 5\right)$