Question

The midpoint of segment AB is M(26, -111). The coordinates of one endpoint is

A(31, 25). Find the coordinate of endpoint B

Answer 1

`\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{31}~,~\stackrel{y_1}{25})\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+31}{2}~~,~~\cfrac{y+25}{2} \right)=\stackrel{\stackrel{midpoint}{M}}{(26,-111)}\implies \begin{cases} \cfrac{x+31}{2}=26\\[0.8em] x+31=52\\ \boxed{x=21}\\[-0.5em] \hrulefill\\ \cfrac{y+25}{2}=-111\\[0.8em] y+25=-222\\ \boxed{y=-197} \end{cases}`

Answer 2

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