# P is the midpoint of the line segment AB. The coordinates of P are (5,-6). The coordinates of A are (-1,10). How do you find the coordinates of B?

##### 1 Answer
Nov 19, 2015

$B = \left({x}_{2} , {y}_{2}\right) = \left(11 , - 22\right)$

#### Explanation:

If one end-point$\left({x}_{1} , {y}_{1}\right)$ and mid-point$\left(a , b\right)$ of a line-segment is known, then we can use mid-point formula to find the second end-point#(x_2, y_2).

$\left({x}_{2} , {y}_{2}\right) = \left(2 a - {x}_{1} , 2 b - {y}_{1}\right)$

Here,
$\left({x}_{1} , {y}_{1}\right) = \left(- 1 , 10\right)$
and
$\left(a , b\right) = \left(5 , - 6\right)$

So,
$\left({x}_{2} , {y}_{2}\right) = \left(2 \textcolor{red}{\left(5\right)} - \textcolor{red}{\left(- 1\right)} , 2 \textcolor{red}{\left(- 6\right)} - \textcolor{red}{10}\right)$
$\left({x}_{2} , {y}_{2}\right) = \left(10 + 1 , - 12 - 10\right)$
$\left({x}_{2} , {y}_{2}\right) = \left(11 , - 22\right)$