Q.

The coplanar points (3, 2, 5), (2, 1, 1), (–1, 4, 1), (0, 5, 5) forms a

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a

rectangle

b

square

c

parallelogram

d

rhombus

answer is B.

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Detailed Solution

The given points are A3,2,5,B2,1,1,C-1,4,1,D0,5,5

Observing the options, let us find the lengths of adjacent sides AB,AD and diagonalas AC,BD

Hence, AB=2-32+1-22+1-52=1+1+16=18

AD=0-32+5-22+5-52=9+9+0=18

Since the adjacent sides are equal, so that the figure formed by the given vertices are either square or Rhombus

Let us find the lengths of the diagonals

AC=-1-32+4-22+1-52=16+4+16=6

BD=0-22+5-12+5-12=16+4+16=6

Diagonals are also equal

Hence, the figure formed by the given four points is square. 

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