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BITSAT 2021 Paper

Section: Mathematics

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Question : 114 of 150

Marks: +1, -0

The points

(0,7,10),(-1,6,6)

(-4,9,6)

form

a right angled isosceles triangle
a scalene triangle
a right angled triangle
an equilateral triangle

Solution:

Let

P(0,7,10), Q(-1,6,6)

and

R(-4,9,6)

be the vertices of a triangle

Here,

PQ=\sqrt{1+1+16}=3\sqrt{2}

QR=\sqrt{9+9+0}=3\sqrt{2}

PR=\sqrt{16+4+16}=6

Now,

PQ^2+QR^2=(3\sqrt{2})^2+(3\sqrt{2})^2=36=(PR)^2

Therefore,

\Delta PQR

is a right angled triangle at Q. Also,

OQ=QR

.

Hence,

\Delta PQR

is a right angled isosceles triangle.

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