The coordinates of quadrilateral ABCD are A(-1,-5), B(8,2), C(11,13), and D(2,6). Using coordinate geometry, prove that quadrilateral ABCD is a rhombus

The quadrilateral ABCD is a rhombus.

Step-by-step explanation:

A rhombus is a quadrilateral having equal sides.

If ABCD is a rhombus then,

AB = BC = CD =  DA

It is provided that the coordinates of the rhombus ABCD are:

A = (-1, -5)

B = (8, 2)

C = (11, 13)

D = (2, 6)

Use the distance formula to compute the lengths of AB, BC, CD and DA.

The distance formula is:

Compute the length of AB:

Compute the length of BC:

Compute the length of CD:

Compute the length of DA:

Thus, the lengths AB, BC, CD and DA are equal, i.e. all sides are of length 11.4.

Hence proved that the quadrilateral ABCD is a rhombus.

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