Question

3) If the points A (1,-2),B(2,3),C(a,2) and D(-4,b) form a parallelogram, find the value of a and B.​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

ANSWER

Consider the given points A(1,−2),B(2,3),C(0,2) and D(−4,−3)

Since ABCD form a parallelogram, the midpoint of the diagonal AC should coincide with the midpoint of BD.

Mid point of AC= Mid point of BD

[21+a,2−2+2]=[22−4,23−3]

[2a+1,0]=[2−2,0]

Since the mid points coincide, we have

21+a=a

⇒a+1=−2

⇒a=−2−1

⇒a=−3

Now, area of ΔABC

=21∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣

=21∣1(3−2)+2(2−(−2))+<