Do the points $\displaystyle \mathrm{P}(1,0), \mathrm{Q}(-5,0)$ and $\displaystyle \mathrm{R}(-2,5)$ form a triangle ? If so, name the type of triangle formed.

\[\left.\begin{array}{l} \mathrm{PQ}=\sqrt{(-5-1)^{2}+(0-0)^{2}}=6 \\ \mathrm{QR}=\sqrt{(-2+5)^{2}+(5-0)^{2}}=\sqrt{34} \text { or } 5.8 \\ \mathrm{PR}=\sqrt{(-2-1)^{2}+(5-0)^{2}}=\sqrt{34} \text { or } 5.8 \end{array}\right\} \] Since sum of any two sides is greater than the third side, ∴ Points P, Q and R form a triangle. \[\mathrm{QR}=\mathrm{PR} \Rightarrow \mathrm{PQR} \text { forms an isosceles triangle. } \]