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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.

A
a=1,h=2
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B
a=1,h=1
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C
a=3,h=1
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D
a=2,h=3
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Solution

The correct option is B a=3,h=1
Given that ABCD is a parallelogram with A(x1,y1)=(1,2),B(x2,y2)=(2,3)
C(x3,y3)=(a,2) and D(x4,y4)=(4,3).
The ordinates of A(x1,y1)=(1,2) & B(x2,y2)=(2,3) are same which is 3.
ABx-axis............(i) and
AB=CD= difference between the abscissa
=(x2x1)=(21) units =1 unit ...........(ii)
Also AB=x3x1=a2 .......(iii)
from (i) & (ii) a2=1
a=3
Again ABCD ....(opposite sides of a parallelogram.)
So, ABCDx-axis.
the height h=mn between AB and CD will be the difference between the respective ordinates i.e. d=y4y1ord=y3y2
So, h=mn=(32) unit =1 unit or |23| unit =1 unit

140944_81272_ans_0291954d73a8451cb0d7609ba45cf154.png

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