Question

If A ( 3x,x-1) ,B(3x+2,x),C(3x+3,x+2),
D(3x+1,x+1) are the vertices of quadrilateral ABCD Show that quadrilateral ABCD is a parallelogram.
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Answer 1

) Given A(6,1)B(8,2)C(9,4)D(7,3)

AB=(8−6)2+(2−1)2

=22+12=5

[∵ Distance =(x2−x1)2+(y2−y1)2

BC=(9−8)2+(4−2)2

=12+22=5

CD=(7−9)2+(3−4)2

=(2)2+(−1)2=5

DA=(7−6)2+(3−1)2

=12+22=5

∴AB=BC=CA=DA

ABCD is a parallelogram.