Explanation:
(B):
Let \(A B=A C\)
Slope of equation \(\mathrm{AB}=7\)
Slope of equation \(\mathrm{AC}=-1\)
Let \(m\) be the slope of \(B C\).
Then,
\(\frac{m-7}{1+7 m}= \pm \frac{m+1}{m-1}\)
Taking +ve sign,
\(m^{2}-8 m+7=7 m^{2}+8 m+1\)
\(-6 m^{2}-16 m+6=0\)
\(3 m^{2}+8 m-3=0\)
\(3 m^{2}+9 m-m-3=0\)
\((m+3)(3 m-1)=0\)
\(m=-3, \frac{1}{3}\)
Now, the equation of line passing through \((1,-10)\) is, \(\mathrm{y}+10=\mathrm{m}(\mathrm{x}-1)\)
Hence, the equation of third side is,
\(y+10=-3(x-1) \text { and } y+10=\frac{1}{3}(x-1)\)
\(3 x+y+7=0 \text { and } x-3 y-31=0\)
\(\therefore\) equation of third side is \(x-3 y=31\)