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.
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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.
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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))+<