Question

Prove that we get a right angled triangle by joining the points (2, 1), (3, 4), (−3, 6).

Answer 1

Let the given points be A (2, 1), B (3, 4) and C (−3, 6).

We know that distance between two points is given by:

D =

Now, AB =

⇒ AB² = 10 ……… (1)

BC =

⇒ BC² = 40 ……… (2)

CA =

CA² = 50 ……… (3)

From (1), (2) and (3), we have:

50 = 40 + 10

i.e. CA² = BC² + AB²

Therefore, the points A, B and C follow the Pythagoras theorem.

Thus, the points A, B and C form a right angled triangle, right-angled at B.