Given: Points are A(3, 6, 9), B(10, 20, 30) and C(25, -41, 5)

To check: the triangle formed by given points is a right-angled triangle or not

A right-angled triangle is a triangle which satisfies Pythagoras Theorem

Formula used:

The distance between any two points (a, b, c) and (m, n, o) is given by,

Therefore,

The distance between A(3, 6, 9) and B(10, 20, 30) is AB,

Distance between B(10, 20, 30) and C(25, -41, 5) is BC,

Distance between A(3, 6, 9) and C(25, -41, 5) is AC,

AB² + BC²

= 686 + 4571

= 5257

AC²

AB² + AC²

= 686 + 2709

= 3395

BC²

AC² + BC²

= 2709 + 4571

= 7280

AB²

As, AB² + BC² AC²

AC² + BC² AB²

AB² + AC² BC²

Thus, Δ ABC is not a right angled triangle