# In the standard (x,y) coordinate plane, the midpoint of AB is (3,–4) and A is located at (2,–3), what is the coordinate of B?

May 28, 2015

If $\text{M}$ is the midpoint of $\text{AB}$
then $\Delta y \left(A \text{ to " M) = Delta y (M " to } B\right)$
and $\Delta x \left(A \text{ to " M) = Delta x (M " to } B\right)$

Since $A$ is located at $\left(2 , - 3\right)$
and $M$ is located at $\left(3 , - 4\right)$

$\Delta y \left(A \text{ to } M\right) = \left(- 4\right) - \left(- 3\right) = - 1$
and
$\Delta x \left(A \text{ to } M\right) = 3 - 2 = 1$

$B$ is located at $\left({M}_{x} + \Delta x , {M}_{y} + \Delta y\right)$
$= \left(3 + 1 , - 4 + \left(- 1\right)\right)$
$= \left(4 , - 5\right)$