Question

The vertices of quadrilateral ABCD are A(3,0), B(4,3), C(7,3), D(6,0).
(a) Prove by means of coordinate geometry, that quadrilateral ABCD is a parallelogram
(b) Prove that ABCD is not a rhombus

Answer 1

(a)

the side AB is 3 units in length and BC is 3 units in length... opposite sides are equal and parallel,

while AB and CD have length

\[AB, CD = \sqrt{10}\]

opposite sides equal and parallel ( found by using the distance formula)

(b) all side not equal in length... see above for details

Answer 2

to prove it's a parallelogra, just prove slopes of opposite sides are equal.

To prove ABCD is not a rhombus, use the distance formula to find the length of all sides.
if they are not all the same length, ABCD is not a rhombus.