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Question

If the points A(1, -2) , B (2,3) , C (a,2) and D (-4,-3) form a parallelogram , find the value of a and height of the parallelogram taking AB as base .

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Solution

Since diagonals of a parallelogram bisect eachother.
Coordinates of the midpoint of AC = coordinates of the midpoint of BD.
a+12,2-22=-4+22,-3+32a+12,0=-1,0On comparing,a+12=-1a=-3Area of the ABC isA=1213-2+22+2-3-2-3A=121+8+15A=12 sq. units

Since, ABCD is a parallelogram,
Area of ABCD = 2 × area of triangle ABC = 2 × 12 = 24 sq. units
Height of the parallelogram is area of the parallelogram divided by its base.
Base AB is
AB=1-22+-2-32=12+52=26Height = 2426=12226

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