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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= (x2x1)2 + (y2y1)2 + (z2z1)2

so,AB=(0+1)2 + (76)2 + (106)2 = 18 = 32

similarly,BC 32 & AC=6

clearly,we see that AB2 + BC2 = AC2

(32)2 + (32)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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