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4. The coordinates of a quadrilateral composed in quadrant of the coordinate plane are (0, 0), (0, c), (b, c), and (b,0). What is the most accurate classification of the quadrilateral? a. Trapezoid b. Rectangle C Barallelogram B D E

4. The coordinates of a quadrilateral composed in quadrant of the coordinate plane are (0, 0), (0, c), (b, c), and (b,0). What is the most accurate classification of the quadrilateral? a. Trapezoid b. Rectangle C Barallelogram B D E

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Question 4: Classification of Quadrilaterals** **Problem Statement:** The coordinates of a quadrilateral composed in the first quadrant of the coordinate plane are (0, 0), (0, c), (b, c), and (b, 0). What is the most accurate classification of the quadrilateral? **Options:** a. Trapezoid b. Rectangle c. Parallelogram d. Square **Answer Section:** A multiple-choice answer is provided below the question. The choices given are labeled A, B, C, D, and E. Each label is encircled, and the label corresponding to option (b) Rectangle is filled in, indicating that option (b) is selected as the correct answer. **Explanation:** The quadrilateral formed by the given coordinates can be analyzed as follows: - The points (0, 0) to (0, c) form a vertical side of length c. - The points (0, c) to (b, c) form a horizontal side of length b. - The points (b, c) to (b, 0) form another vertical side of length c. - The points (b, 0) to (0, 0) form the other horizontal side of length b. Since opposite sides are equal and parallel, and all angles are right angles, the quadrilateral meets the criteria of both a rectangle and a parallelogram. However, the most specific classification given the side lengths and angles is option (b) Rectangle.
Transcribed Image Text:**Question 4: Classification of Quadrilaterals** **Problem Statement:** The coordinates of a quadrilateral composed in the first quadrant of the coordinate plane are (0, 0), (0, c), (b, c), and (b, 0). What is the most accurate classification of the quadrilateral? **Options:** a. Trapezoid b. Rectangle c. Parallelogram d. Square **Answer Section:** A multiple-choice answer is provided below the question. The choices given are labeled A, B, C, D, and E. Each label is encircled, and the label corresponding to option (b) Rectangle is filled in, indicating that option (b) is selected as the correct answer. **Explanation:** The quadrilateral formed by the given coordinates can be analyzed as follows: - The points (0, 0) to (0, c) form a vertical side of length c. - The points (0, c) to (b, c) form a horizontal side of length b. - The points (b, c) to (b, 0) form another vertical side of length c. - The points (b, 0) to (0, 0) form the other horizontal side of length b. Since opposite sides are equal and parallel, and all angles are right angles, the quadrilateral meets the criteria of both a rectangle and a parallelogram. However, the most specific classification given the side lengths and angles is option (b) Rectangle.
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