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Question

The points A(1,−2),B(2,3),C(k,2) and D(−4,−3) are the vertices of a parallelogram. Find the value of k.

A
2
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B
2
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C
3
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D
3
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Solution

The correct option is D 3
We know that diagonals of a parallelogram bisects each other.
So, the co-ordinates A(1,2) B(2,3), C(k,2) and D(4,3)
Mid-point of AC=Mid point of BD
(x1+x22,y1+y22)=(x1+x22,y1+y22)
(1+k2,2+22)=(2+(4)2,3+(3)2)
(1+k2,0)=(22,02)
1+k2=22
2(1+k)=4
2+2k=4
2k=42
2k=6
k=62
k=3
So, the value of K=3.

1191641_1258497_ans_e92d0d06c88c4484b6fe352b9040b446.jpg

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