Q. 174.2( 13 Votes )

The vertices of a

Answer :


The vertices of the given quadrilateral are A(-4,-2) B(2, 6), C(8, 5) and D(9, -7)


The mid point of a line A(x1,y1) and B(x2,y2) is found out by


Now midpoint of AB =


The midpoint of BC =


The midpoint of CD =


Midpoint of DA =


So now we have four points


P(-1,2),Q(5,5.5),R(8.5,-1),S(2.5,-4.5)



Slope of PQ =


Slope of QR =


Slope of RS =


Slope of SP =


Now we can observe that slope of PQ = RS and slope of QR = SP


Which shows that line PQ is parallel to RS and line QR is parallel to SP


Also, the product of two adjacent lines is not equal to -1


Therefore PQRS is a parallelogram.


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