Question

Two equal sides of an isosceles triangle are given by `7x-y+3=0` and `x+y=3`, and its third side passes through the point `(1,-10)`. Find the equation of the third side.

Answer 1

The equation of any line passing through `(1,-10)` is `y+10=m(x-1)`.
Since, it makes equal angles, say `theta`, with the given lines therefore
`tantheta=(m-7)/(1+7m)=(m-(-1))/(1+m(-1))impliesm=(1)/(3)` or `-3`
Hence, the equations of third side are
`y+10=(1)/(3)(x-1)` or `y+10=-3(x-1)`
i.e. `x-3y-31=0` or `3x+y+7=0`