# The midpoint of segment AB is (1, 4). The coordinates of point A are (2,-3). How do you find the coordinates of point B?

Dec 31, 2016

The coordinates of point B are $\left(0 , 11\right)$

#### Explanation:

Midpoint of a segment, whose two end points are $A \left({x}_{1} , {y}_{1}\right)$ and $B \left({x}_{2} , {y}_{2}\right)$ is

$\left(\frac{{x}_{1} + {x}_{2}}{2} , \frac{{y}_{1} + {y}_{2}}{2}\right)$

as $A \left({x}_{1} , {y}_{1}\right)$ is $\left(2 , - 3\right)$, we have ${x}_{1} = 2$ and ${y}_{1} = - 3$

and a midpoint is $\left(1 , 4\right)$, we have

$\frac{2 + {x}_{2}}{2} = 1$

i.e. $2 + {x}_{2} = 2$ or ${x}_{2} = 0$

$\frac{- 3 + {y}_{2}}{2} = 4$

i.e. $- 3 + {y}_{2} = 8$ or ${y}_{2} = 8 + 3 = 11$

Hence coordinates of point $B$ are $\left(0 , 11\right)$