The best selection for the quadrilateral with the given vertices is: parallelogram.
Recall:
Parallel lines are lines do not intersect and they are equal distant apart.
The opposite side of a parallelogram are of equal length.
Thus, the points of the vertices of the quadrilateral has been graphed in the diagram shown below:
Point A (-2,0)
Point B (0,4)
Point C (6,4)
Point D (4,0)
Find the distance between each vertices using the distance formula: [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Distance between Point A (-2,0) and Point B (0,4):
[tex]AB = \sqrt{(0 -(-2))^2 + (4 - 0)^2} \\\\\mathbf{AB = \sqrt{20} }[/tex]
Distance between Point B (0,4) and Point C (6,4):
[tex]BC = \sqrt{(6 - 0)^2 + (4 - 4)^2} \\\\\mathbf{BC = 6 }[/tex]
Using the same distance formula, CD = √20 while AD = 6
This means that the opposite sides of the quadrilateral with the given vertices are equal in length. Parallelogram has two pairs of equal sides.
Therefore, the best selection for the quadrilateral with the given vertices is: parallelogram.
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