Question

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

Answer 1

Answer :

Let the A(3, 0), B(6, 4) and C(- 1, 3) are three vertices.

Now using distance formula for two points A(x1, y1) and B(x2, y2)

We have

= 5 units

= 5 units

Now, AB > BC = AC

Therefore, if ABC is a right angled triangle. AB should be hypotenuse. BC and AC should be other two sides.(i.e. perpendicular and base)

And should satisfy the Pythagoras theorem, that says

(hypotenuse)2 = (perpendicular)2 + (base)2

AB2 = BC2 + AC2

Taking RHS

= LHS

Hence ABC is a right angled triangle