Question

Name the type of triangle $PQR$ formed by the points $P(-\sqrt{2},\sqrt{2}),Q(-\sqrt{2},-\sqrt{2})$ and $R(-\sqrt{6},\sqrt{6})$.

Answer 1

$\begin{array}{c}Byusingdistanceformula\\ \Rightarrow PQ=\sqrt{0^2+{\left(2\sqrt{2}\right)}^2}=2\sqrt{2}unit\\ \Rightarrow QR=\left[\sqrt{{\left(-\sqrt{6}+\sqrt{2}\right)}^2+{\left(\sqrt{6}+\sqrt{2}\right)}^2}=\sqrt{6+2-2\sqrt{12}+2\sqrt{12}+6+2}\right]\\ \Rightarrow QR=\sqrt{16}=4unit\\ \Rightarrow RP=\sqrt{{\left(-\sqrt{6}+\sqrt{2}\right)}^2+\left(\sqrt{6}-\sqrt{2}\right)}\\ \Rightarrow RP=\sqrt{6-2\sqrt{12}+2+6-2\sqrt{12}+2}\\ \Rightarrow RP=\sqrt{16-4\sqrt{12}}unit\\ \therefore PQ\ne QR\ne RP\\ Itisscalenetriangle.\end{array}$