Question

study the coordinate plane below. a certain polygon has its vertices at the following points: (2,5), (4,7), (7,7), and (9,5) what is the best description of this polygon? a. parallelogram b. trapezoid c. pentagon d. rhombus

Explanation:

Step1: Recall the properties of each polygon

• Parallelogram: A quadrilateral with two pairs of parallel sides.
• Trapezoid: A quadrilateral with at least one pair of parallel sides.
• Pentagon: A five - sided polygon.
• Rhombus: A parallelogram with all sides equal.

Step2: Analyze the given polygon

The given polygon has four vertices \((2,5)\), \((4,7)\), \((7,7)\), and \((9,5)\), so it is a quadrilateral (eliminating option C).
The slope of the line passing through \((2,5)\) and \((4,7)\) is \(m_1=\frac{7 - 5}{4 - 2}=\frac{2}{2} = 1\).
The slope of the line passing through \((4,7)\) and \((7,7)\) is \(m_2=\frac{7 - 7}{7 - 4}=0\).
The slope of the line passing through \((7,7)\) and \((9,5)\) is \(m_3=\frac{5 - 7}{9 - 7}=\frac{-2}{2}=-1\).
The slope of the line passing through \((9,5)\) and \((2,5)\) is \(m_4=\frac{5 - 5}{2 - 9}=0\).
We can see that there is only one pair of parallel sides (the sides with slope \(0\)).

Answer:

B. trapezoid