The equal sides of an isosceles triangle are given by equations $7 x-y+3=0$ and $x+y-3=0$. If the slope $m$ of the third side is an integer, then $\mathrm{m}=$

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Aicharya · Accepted Answer

Let $	riangle \mathrm{ABC}$ be the isosceles triangle where $\mathrm{AB}=\mathrm{AC}$ Hence Bisector of Angle $\angle B A C$ will also be the perpendicular on line $\mathrm{BC}$. Let $m_1$ and $m$ be the slopes of bisector lines AP and line $B C$ respectively. Equation of Bisector lines (AP) are $ \begin{aligned} & \frac{7 x-y+3}{\sqrt{49+1}}= \pm \frac{(x+y-3)}{\sqrt{(1)+(1)}} \ & \Rightarrow x-3 y+6=0 	ext { and } 3 x+y-12=0 \end{aligned} $ Here $m_1=\frac{1}{3}$ Since AP $\perp$ BC $ 	herefore m_1 \cdot m=-1 $ $ m=-3 $ Here $m_1=-3$ Since AP $\perp$ BC $ 	herefore m_1 \cdot m=-1 $ $ \Rightarrow m=\left(\frac{1}{3}ight) $ Since $m$ is integer (given) Hence $m=-3$

The equal sides of an isosceles triangle are given by equations $7 x-y+3=0$ and $x+y-3=0$. If the slope $m$…

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