Question

Point M is the midpoint of AB. If the coordinates of M are (2,8) and the coordinates of A are (10,12),what are the coordinates of B?

Answer 1

$~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{10}~,~\stackrel{y_1}{12})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x + 10}{2}~~~ ,~~~ \cfrac{ y + 12}{2} \right)~~=~~\stackrel{M}{(2,8)}\implies \begin{cases} \cfrac{x+10}{2}=2\\[1em] x+10=4\\ \boxed{x=-6}\\[-0.5em] \hrulefill\\ \cfrac{y+12}{2}=8\\[1em] y+12=16\\ \boxed{y=4} \end{cases}$