Question

The midpoint of MO is N (15, 12). M is at (-4, 9) what is the coordinate of O?

Answer 1

The formula of the midpoint of MO:
$N\left(\dfrac{x_M+x_O}{2};\ \dfrac{y_M+y_O}{2}\right)$

We have N(15; 12) and M(-4; 9), O(x; y). Substitute:
$(15;\ 12)=\left(\dfrac{-4+x}{2};\ \dfrac{9+y}{2}\right)\\\\\dfrac{-4+x}{2}=15\ \ \ \ |\cdot2\\\\-4+x=30\ \ \ |+4\\\\x=34\\\\\dfrac{9+y}{2}=12\ \ \ \ |\cdot2\\\\9+y=24\ \ \ |-9\\\\y=15$
Your answer is  $N(34;\ 15)$