Question

Choose the most correct statement given that Quadrilateral ABCD has vertices A(2, 1),B(2, 4), C(7, 4), and D(6, 1).

Answer 1

Quadrilateral ABCD is not a rectangle, square, or parallelogram because both pairs of opposite sides are not parallel or congruent.

Explanation:

Consider quadrilateral ABCD with its vertices at:

A(2, 1), B(2, 4), C(7, 4), and D(6, 1).

Line AD is a horizontal line passing through y=1.

`AD=|6-2|=4\text{ units}`

Similarly, line BC is a horizontal line passing through y=4.

`BC=|7-2|=5\text{ units}`

Since the opposite sides are not equal, the quadrilateral ABCD is not a rectangle, square, or parallelogram because both pairs of opposite sides are not parallel or congruent.

The last option is correct.

Note: The result can be confirmed from the graph below: