Question

M (5,7) is the midpoint of RS the coordinates of s are (6,9) what are coordinates of r

Answer 1

`\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ R(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad S(\stackrel{x_2}{6}~,~\stackrel{y_2}{9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x+6}{2}~~,~~\cfrac{y+9}{2} \right)=\stackrel{\stackrel{midpoint}{M}}{(5,7)}\implies \begin{cases} \cfrac{x+6}{2}=5\\[1em] x+6=10\\ \boxed{x=4}\\[-0.5em] \hrulefill\\ \cfrac{y+9}{2}=7\\[1em] y+9=14\\ \boxed{y=5} \end{cases}`