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tester [92]
3 years ago
6

One Endpoint is 9,18 and the midpoint is 14,16 what the other end point

Mathematics
1 answer:
Valentin [98]3 years ago
7 0
\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ 9}}\quad ,&{{ 18}})\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+9}{2}~,~\cfrac{y+18}{2} \right)=\stackrel{\textit{midpoint}}{(14,16)}\implies 
\begin{cases}
\cfrac{x+9}{2}=14\\\\
x+9=28\\
\boxed{x=19}\\
-------\\
\cfrac{y+18}{2}=16\\\\
y+18=32\\
\boxed{y=14}
\end{cases}
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