Question

Find the type of triangle formed by the points P(-5,6), Q(-4,-2) and R(7,5).

Answer 1

Given vertices $P(-5,6);Q(-4,-2);R(7,5)$

$PQ=\sqrt{(-5+4{)}^2+(-2-6{)}^2}=\sqrt{1+64}=\sqrt{65}QR=\sqrt{(7+4{)}^2+(5+2{)}^2}=\sqrt{121+49}=\sqrt{170}PR=\sqrt{(7+5{)}^2+(5-6{)}^2}=\sqrt{144+1}=\sqrt{145}$

Since the length of sides are different the triangle is Scalene triangle.