Q. 153.9( 26 Votes )

# If A(&ndash

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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