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

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Aicharya · Accepted Answer

Given equation of sides are $\begin{array}{l} 7 x-y+3=0 \quad \ldots (i)\ x+y-3=0 \quad \ldots (ii) \end{array}$ Equation of angle bisectors of Eqs. (i) and (ii) are $\begin{aligned} & \frac{7 x-y+3}{\sqrt{49+1}}= \pm \frac{x+y-3}{\sqrt{1+1}} \ & \frac{7 x-y+3}{\sqrt{50}}= \pm \frac{x+y-3}{\sqrt{2}} \ & \frac{7 x-y+3}{5}= \pm \frac{x+y-3}{1} \ & \therefore \quad \frac{7 x-y+3}{5}=(x+y-3) \ & \text {or } \quad \frac{7 x-y+3}{5}=-(x+y-3) \ & 7 x-y+3=5 x+5 y-15 \ & \text {or } \quad 7 x-y+3=-5 x-5 y+15 \ & \Rightarrow \quad 2 x-6 y+12=0 \ & \text {or } \quad 12 x+4 y-12=0 \ & \Rightarrow \quad x-3 y+6=0 \text { or } 3 x+y-3=0 \ & \text {Slope }=\frac{1}{3} \text {, Slope }=-3 \text { (integer) } \end{aligned}$ Here, third side is parallel to one angle bisector. $\therefore$ Required slope of third side is -3 .

Two equal sides of an isosceles triangle are given by \(7 x-y+3=0\) and \(x+y-3=0\). If the slope \(m\) of…

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