Q. 55.0( 2 Votes )

# The quadrilateral formed by points (–1, 1), (0, –3), (5, 2) and (4, 6) will be:

A. square

B. rectangular

C. rhombus

D. parallelogram

Answer :

We have A → (–1, 1)

B → (0, –3)

C → (5, 2)

D → (4, 6)

Using the distance formula,

AB =

=

=

=

BC =

=

=

=

CD=

=

=

=

DA =

=

=

=s

We find that AB = CDand BC = DA.

The oppposite pairs of sides are equal for the given quadrilateral.

Consider the diagonals, AC and BD.

AC =

=

=

=

BD =

=

=

=

Since the diagonals are not equal, the given quadrilateral is not a rectangle.

(This is also visible from the figure since angles are not 90°.)

⇒ ABCD is a parallelogram.

∴ The correct option is **D**.

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