How do you find the midpoint of (10,-3), (-8,-5)?

Mar 10, 2018

$\left(1 , - 4\right)$

Explanation:

Vertically: $\left({y}_{2} - {y}_{1}\right) = \left(y - {y}_{1}\right)$

${y}_{1} + {y}_{2} = 2 y$

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

Horizontally: $\left({x}_{2} - {x}_{1}\right) = \left(x - {x}_{1}\right)$

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

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

$\therefore$ The coordinates of the midpoint $M \left(x , y\right)$ are given by:
$\left(x , y\right) = \left(\frac{{x}_{1} + {x}_{2}}{2} , \frac{{y}_{1} + {y}_{2}}{2}\right)$

$\left(x , y\right) = \left(\frac{10 + \left(- 8\right)}{2} , \frac{\left(- 3\right) + \left(- 5\right)}{2}\right)$

$\left(x , y\right) = \left(\frac{2}{2} , \frac{- 8}{2}\right)$

$\left(x , y\right)$ = (1,-4)