Answer :

Given:

Parallelogram ABCD


A( – 2, 1), B(a, 0), C(4, b), D(1, 2)


Now, Midpoint of AC = Midpoint of BD


( diagonals of a parallelogram bisect each other)


Using Midpoint Formula i.e.


The midpoint of the segment joining and is given by


Putting values,


The midpoint of AC


The midpoint of BD 
Now,

⇒ a + 1 = 2
⇒ a = 1
And,

⇒ 1 + b = 2
⇒ b = 1


a = 1 and b = 1

So, coordinates are A( – 2, 1), B(1, 0), C(4, 1), D(1, 2).

Using Distance Formula i.e.

Distance between (x1, y1) and (x2, y2 ) is given by:


D = 


Now,




And,



OR



Ar(ABCD) = Ar(ABC) + Ar(ADC)


The area of the triangle with points (x1 , y1), (x2 , y2) and (x3 , y3) is:



• Ar(Δ ABC)


• Ar(Δ ADC)


So, Ar(ABCD) = Ar(Δ ABC) + Ar (Δ ADC)


= 72 sq. units
 

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