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?

Answer :

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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