Question

Show that the points A(0,0),B(6,0),D(9,4) and C(3,4) are the vertices of a parallelogram taken in order​

Answer 1

Given :   the points A(0,0),B(6,0),D(9,4) and C(3,4) are the vertices of a parallelogram taken in order​

To Find : Show

Solution:

If both pair of opposite sides are Equal in Length then a quadrilateral is a parallelogram

If both pair of opposite sides are parallel  then a quadrilateral is a parallelogram

If one pair of opposite side are parallel and equal in length then Quadrilateral is a parallelogram

If Diagonal bisects Each other then quadrilateral is a parallelogram

Using last case

A(0,0),B(6,0),D(9,4) and C(3,4) are taken in order

so diagonals are AD and BC

Mid point of AD = ( 0 + 9)/2 , ( 0 + 4)/2

= 9/2 , 2

Mid point of BC   = (6 + 3)/2 , ( 0 + 4)/2

= 9/2 , 2

Hence mid point of both diagonals are same

Hence diagonals bisects each other

Hence shown that these are vertices of a parallelogram

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