Q. 195.0( 1 Vote )

# Are the points A(3, 6, 9), B(10, 20, 30) and C(25, -41, 5), the vertices of a right-angled triangle?

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

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