Q. 114.3( 3 Votes )

If the vertices of a quadrilateral are (1, 4), (–5, 4), (–5, –3) and (1, –3), then find the type of quadrilateral.

Answer :

We have A (1, 4)


B (–5, 4)


C (–5, –3)


D (1, –3)


Using the distance formula,


AB =


=


=


=6


BC =


=


=


= 7


CD =


=


=


=


= 6


DA =


=


=


= 7


The opposite sides are equal in length.


Consider the diagonals, AC and BD.


AC =


=


=


=


BD =


=


=


=


Since the diagonals are also equal, the given quadrilateral is a rectangle.


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