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

The equation of any straight line passing through $P(2,1)$ can be written as $$\frac{y-1}{x-2}=m$$ where $m$ is the gradient/slope

Now as $\angle RPQ=90^\circ$ and $|PQ|=|RP|$

Using Isosceles Triangles have Two Equal Angles, $\displaystyle \angle PQR=\angle QRP=45^\circ$

If the angle between two lines with slope $m_1,m_2$ is $\phi$

$\displaystyle\tan\phi=\left|\frac{m_1-m_2}{1+m_1m_2}\right|$

In our case, $\displaystyle \phi=45^\circ$

we can set $m_1=m$(to be determined) and the $m_2,$ the gradient of $\displaystyle QR:2x+y=3\iff y=-2x+3$ is $-2$