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If the coordinates of the vertices of the triangle $A B C$ be $(-1,6),(-3,-9)$, and $(5,-8)$ respectively, then the equation of the median through $C$ is
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Verified Answer
The correct answer is:
$13 x+14 y+47=0$
Let the Median be CD
Point of \(D\) is \((x, y)\)
Now, \(x=\frac{-3-1}{2}, x=-2\) and \(y=\frac{6-9}{2}=-\frac{3}{2}\)
Slope of \(\mathrm{CD}\) is,
\(=\frac{8-\frac{3}{2}}{5+2}=\frac{13}{14}\)
Equation:
\(C D=y+8=\frac{13}{14}(\mathrm{x}-5)\)
So the equation of Median,
\(13 \mathrm{x}-14 \mathrm{y}-47=0\)
Point of \(D\) is \((x, y)\)
Now, \(x=\frac{-3-1}{2}, x=-2\) and \(y=\frac{6-9}{2}=-\frac{3}{2}\)
Slope of \(\mathrm{CD}\) is,
\(=\frac{8-\frac{3}{2}}{5+2}=\frac{13}{14}\)
Equation:
\(C D=y+8=\frac{13}{14}(\mathrm{x}-5)\)
So the equation of Median,
\(13 \mathrm{x}-14 \mathrm{y}-47=0\)
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