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.
∴AB∥x-axis............(i) and
AB=CD= difference between the abscissa
=(x2−x1)=(2−1) units =1 unit ...........(ii)
Also AB=x3−x1=a−2 .......(iii)
∴ from (i) & (ii) a−2=1
⇒a=3
Again AB∥CD ....(opposite sides of a parallelogram.)
So, AB∥CD∥x-axis.
∴ the height h=mn between AB and CD will be the difference between the respective ordinates i.e. d=y4−y1ord=y3−y2
So, h=mn=(3−2) unit =1 unit or |2−3| unit =1 unit