Question

If M is the midpoint of XY, find the coordinates of X if M(-3,-1) and Y(-8,6)

Answer 1

$\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) X&({{ a}}\quad ,&{{ b}})\quad % (c,d) Y&({{ -8}}\quad ,&{{ 6}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)$

$\bf \left( \cfrac{-8+a}{2}~,~\cfrac{6+b}{2} \right)=\stackrel{M}{(-3,-1)}\implies \begin{cases} \cfrac{-8+a}{2}=-3\\\\ -8+a=-6\\ \boxed{a=2}\\ ----------\\ \cfrac{6+b}{2}=-1\\\\ 6+b=-2\\ \boxed{b=-8} \end{cases}$