Question

prove that the point ( 3 , 0 ) , ( 6 , 4 ) and ( - 1 , 3 ) are the verticess of a right angled isosceles triangle .​

Answer 1

Distance Formula

→ √[(x₂ - x₁)² + (y₂ - y₁)]

AB = √[(6 - 3)² + (4 - 0)²] = 5

BC = √[(6 + 1)² + (4 - 3)²] = 5√2

CA = √[(3 + 1)² + (0 - 3)²] = 5

Hence AB = BC, thus it's an isosceles ∆.

Now, H² = B² + P²

→ (5√2)² = 5² + 5²

→ 25 × 2 = 25 + 25

→ 50 = 50

→ L.H.S = R.H.S

Q.E.D