Question

show that points (0,1,2)(2,5,8)(5,6,6)and (3,2,0) from a parallelogram
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Answer 1

Let A(0-1), B(6,7), C(-2,3) and D(8,3) be the given points. Then

,AD=

(8−0)

2

+(3+1)

2

=

64+16

=4

5

BC=

(6+2)

2

+(7−3)

2

=

64+16

=4

5

AC=

(−2−0)

2

+(3+1)

2

=

4+16

=2

5

and,

BD=

(8−6)

2

+(3−7)

2

=

4+6

=2

5

∴AD=BCandAC=BD

So, ADBC is a parallelogram

Now

AB=

(6−0)

2

+(7+1)

2

=

36+64

=10

and,CD=

(8+2)

2

+(3−3)

2

=10

Clearly,AB

2

=AD

2

+DB

2

andCD

2

=CB

2

+BD

2

Hence, ADBC is a rectangle.

Now

,Area of rectangle ADBC=AD×DB=(4

5

×2

5

)sq.