Let $PQR$ be a right angled isosceles triangle right angled at $P$ (2, 1). If the equation of the line $QR$ is $2x + y = 3$, then the equations representing the pair of lines $PQ$ and $PR$ is

Let the slopes of $PQ$ and $PR$ be $m\text{ and }-1/m$ respectively. Since $PQR$ is an isosceles triangle  $P Q R=$$\text{ PRQ }$

$\left|\frac{m+2}{1-2m}\right|=\left|\frac{-\frac{1}{m}+2}{1+\frac{2}{m}}\right|$

[∵ slope of QR = – 2]

$\Rightarrow m + 2 = \pm (1 – 2m) fi m = 3 or – 1/3$

So the equations of $PQ$ and $PR$ are

$(y-1)=3(x-2)\text{ and }y-1=(-1/3)(x-2)$

$\Rightarrow 3x-y=5,x+3y=5$