Question

M(6, 6) is the midpoint of . The coordinates of S are (8, 9). What are the coordinates of R?

Answer 1

$\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) R&({{ x}}\quad ,&{{ y}})\quad % (c,d) S&({{ 8}}\quad ,&{{ 9}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)$

$\bf \left( \cfrac{8+x}{2}~~,~~\cfrac{9+y}{2} \right)=\stackrel{midpoint}{M(6,6)}\implies \begin{cases} \cfrac{8+x}{2}=6\\\\ 8+x=12\\ \boxed{x=4}\\ ----------\\ \cfrac{9+y}{2}=6\\\\ 9+y=12\\ \boxed{y=3} \end{cases}$