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

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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