Question

What is the most precise name for quadrilateral ABCD with vertices A(−1,0), B(4,0), C(5,4), and D(0,4)?

Answer 1

parallelogram

Explanation:

Plot the points on a coordinate plane.

You will see that it is a quadrilateral with 2 pairs of opposite sides parallel. That makes it a parallelogram. Also you will see that adjacent sides are not congruent, so it is not a rhombus. It has no right angles, so it is not a rectangle.

Answer: parallelogram

Answer 2

Answer with explanation:

The vertices of Quadrilateral ABCD are , A(−1,0), B(4,0), C(5,4), and D(0,4).

`AB=√((4+1)^2+0)\\\\AB=5\\\\BC=√((5-4)^2+(4-0)^2)\\\\BC=√(17)\\\\CD=√((5-0)^2+(4-4)^2)\\\\CD=5\\\\DA=√((0+1)^2+(4-0)^2)\\\\AD=√(17)\\\\AC=√((5+1)^2+(4-0)^2)\\\\AC=√(36+16)\\\\AC=√(52)\\\\AC=2√(13)\\\\BD=√((4-0)^2+(0-4)^2)\\\\BD=√(32)\\\\BD=4√(2)`

→Opposite sides are equal,but diagonals are not equal.

That is, AB=CD, and AD=BC.

But, AC≠BD.

Hence the given Quadrilateral is a Parallelogram.