Two equal sides of an isosceles triangle are along -x + 2y = 4 and x + y = 4 .

Question

Two equal sides of an isosceles triangle are along $ -x + 2y = 4 $ and $ x + y = 4 $. If $ m $ is the slope of its third side, then the sum, of all possible distinct values of $ m $, is:

Accepted Answer

$$\begin{aligned}
& \tan \theta=\frac{m-\frac{1}{2}}{1+\frac{1}{2} \cdot m}=\frac{-1-m}{1-m}=\frac{m+1}{m-1} \
& \frac{2 m-1}{2+m}=\frac{m+1}{m-1} \
& 2 m^2-3 m+1=m^2+3 m+2
\end{aligned}$$

$$\begin{aligned}
& m^2-6 m-1=0 \
& \text { sum of root }=6 \
& \text { sum is } 6
\end{aligned}$$

Solutions · 1