# How do you find the midpoint of (-9,-6) (6,6)?

Mar 15, 2016

$\implies {P}_{\text{mid}} \to \left(x , y\right) \to \left(- \frac{3}{2} , 0\right)$

#### Explanation:

Important fact: The mid point on a slope lines up with the mid point of its projection onto an axis.

Thus:

Let ${P}_{1} \to \left({x}_{1} , {y}_{1}\right) \to \left(- 9 , - 6\right)$

Let ${P}_{2} \to \left({x}_{2} , {y}_{2}\right) \to \left(6 , 6\right)$

Mid point is $\frac{{P}_{1} + {P}_{2}}{2} \to \frac{{x}_{1} + {x}_{2}}{2} , \frac{{y}_{1} + {y}_{2}}{2}$

${P}_{\text{mid x}} \to \frac{- 9 + 6}{2} = - \frac{3}{2}$

${P}_{\text{mid y}} \to \frac{- 6 + 6}{2} = 0$

$\implies {P}_{\text{mid}} \to \left(x , y\right) \to \left(- \frac{3}{2} , 0\right)$