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

Answer with explanation:

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

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

→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.

Answer 2

Answer:

parallelogram

Step-by-step 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