Question

Prove that the points, (3,0) (6,4) (-1,3) are vertices of a right angled isosceles triangle.

Answer 1

Let A (3,0) B (6,4) and C (-1,3)
now use distance formula ,
AB=root {(6-3)^2+(4-0)^2}=root (25)=5
BC=root {(-1-6)^2+(3-4)^2}=root (50)
CA =root {((3+1)^2+(-3)^2}=5.

you see ,
BC^2 =AC^2 + AB^2
which is related to Pythagoras theorem .
hence , ABC is the vertices of right angle isoceles triangle .in which A is right angle