Question

AB has a midpoint M at (6, 3). If point A is at (-5, -1) & point B is at (2a - 7, b + 7), find the value of b

Answer 1

`\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-5}~,~\stackrel{y_1}{-1})\qquad B(\stackrel{x_2}{2a-7}~,~\stackrel{y_2}{b+7}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{(2a-7)-5}{2}~~,~~\cfrac{(b+7)-1}{2} \right)=\stackrel{\stackrel{midpoint}{M}}{(6,3)}\implies \begin{cases} \cfrac{(2a-7)-5}{2}=6\\[-0.5em] \hrulefill\\ \cfrac{(b+7)-1}{2}=3\\[0.8em] (b+7)-1=6\\ b+6=6\\ \boxed{b=0} \end{cases}`