# How do you find the coordinates of the other endpoint of a segment with the given N(5,-09), and midpoint M(8, -7.5)?

##### 1 Answer
Aug 12, 2017

$\left(11 , - 14.1\right)$

#### Explanation:

First, let's find the difference between the coordinates of $M$ and $N$:

$R i g h t a r r o w M - N = \left(8 , - 7.5\right) - \left(5 , - 0.9\right)$

$R i g h t a r r o w M - N = \left(8 - 5 , - 7.5 - \left(- 0.9\right)\right)$

$\therefore M - N = \left(3 , - 6.6\right)$

If we add this difference to $M$, we will find the coordinates of the other endpoint $O$ of this segment:

$R i g h t a r r o w O = M + \left(M - N\right)$

$R i g h t a r r o w O = \left(8 , - 7.5\right) + \left(3 , - 6.6\right)$

$R i g h t a r r o w O = \left(8 + 3 , - 7.5 + \left(- 6.6\right)\right)$

$\therefore O = \left(11 , - 14.1\right)$

Therefore, the coordinates of the other endpoint of the segment are $\left(11 , - 14.1\right)$.