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Question

# If the points (0,7,10),(−1,6,6)and(−4,9,6) are the vertices of a triangle, then the triangle is _____

A

Right angled

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B

Isosceles right angled

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C

Equilateral

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D

None of these

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Solution

## The correct option is B Isosceles right angled Let A ≡ (0,7,10),B ≡ (−1,6,6),C ≡ (−4,9,6) Distance between two points (x1,y1,z1) & Q (x2,y2,z2) is PQ= √(x2−x1)2 + (y2−y1)2 + (z2−z1)2 so,AB=√(0+1)2 + (7−6)2 + (10−6)2 = √18 = 3√2 similarly,BC≡ 3√2 & AC=6 clearly,we see that AB2 + BC2 = AC2 (3√2)2 + (3√2)2 = 36 18+18=36 36=36 ∴ ∠ ABC = 90∘ Triangle formed by these coordinates is right angle triangle. Also AB=BC Hence,△ ABC is right angled isosceles triangle option B is correct

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