SeanDGA
contestada

Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint.​ (Hint: Let​ (x,y) be the unknown endpoint. Apply the midpoint​ formula, and solve the two equations for x and​ y.) midpoint ​(-14​,- 17​), endpoint ​(-5​,-4​)

Respuesta :

[tex] \bf ~~~~~~~~~~~~\textit{middle point of 2 points }
\\\\
(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad
(\stackrel{x_2}{-5}~,~\stackrel{y_2}{-4})
\qquad
\left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right)
\\\\\\
\left(\cfrac{-5+x}{2}~~,~~\cfrac{-4+y}{2} \right)~=~\stackrel{\textit{midpoint}}{(-14,-17)}\implies
\begin{cases}
\cfrac{-5+x}{2}=-14\\\\
-5+x=-28\\
\boxed{x=-23}\\[-0.5em]
\hrulefill\\
\cfrac{-4+y}{2}=-17\\\\
-4+y=-34\\
\boxed{y=-30}
\end{cases} [/tex]

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