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stich3 [128]
3 years ago
15

The midpoint of CD is M(-1,-2). One endpoint is C (-9,-4). Find the coordinates of the other endpoint D.

Mathematics
1 answer:
yan [13]3 years ago
6 0
\bf ~~~~~~~~~~~~\textit{middle point of 2 points }\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&C&(~ -9 &,& -4~) 
%  (c,d)
&D&(~ x &,& y~)
\end{array}\qquad
%   coordinates of midpoint 
\left(\cfrac{ x_2 +  x_1}{2}\quad ,\quad \cfrac{ y_2 +  y_1}{2} \right)
\\\\\\
\left( \cfrac{x-9}{2}~~,~~\cfrac{y-4}{2} \right)=\stackrel{midpoint~M}{(-1~~,~~-2)}\implies 
\begin{cases}
\cfrac{x-9}{2}=-1\\\\
x-9=-2\\
\boxed{x=7}\\
----------\\
\cfrac{y-4}{2}=-2\\\\
y-4=-4\\
\boxed{y=0}
\end{cases}
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