# For a line segment AB, one endpoint is A(0,6) and the midpoint is M(4,7) how do you find the coordinates of endpoint B?

Apr 24, 2015

The change in $x$ and $y$ respectively from A at $\left(0 , 6\right)$ to M at $\left(4 , 7\right)$ are

$\Delta {x}_{A M} = 4$
and
$\Delta {y}_{A M} = 1$

Since M is the midpoint between A and B
$\Delta {x}_{M B} = \Delta {x}_{A M}$
and
$\Delta {y}_{M B} = \Delta {y}_{A M}$

B is located at $M + \left(\Delta {x}_{M B} , \Delta {y}_{M B}\right)$

$= \left(4 + 4 , 7 + 1\right) = \left(8 , 8\right)$