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2 years ago

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(-23,10) endpoint (-17,7)

Mathematics

1 answer:

Naily [24]2 years ago

3 0

$\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -17}}\quad ,&{{ 7}})\quad 
% (c,d)
&({{ x}}\quad ,&{{ y}})
\end{array}\qquad
% coordinates of midpoint 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)$

$\bf \left( \cfrac{x-17}{2}~,~\cfrac{y+7}{2} \right)=\stackrel{\textit{midpoint}}{(-23,10)}\implies 
\begin{cases}
\cfrac{x-17}{2}=-23\\\\
x-17=-46\\
\boxed{x=-29}\\
----------\\
\cfrac{y+7}{2}=10\\\\
y+7=20\\
\boxed{y=13}
\end{cases}$

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