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Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5, 4). What is the shape of the quadrilateral
- a)Square
- b)Rectangle but not a square
- c)Rhombus
- d)Parallelogram but not a rhombus
- e)Kite
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5...
The lengths of the four sides, AB, BC, CD and DA are all equal to√41.
Hence, the given quadrilateral is either a Rhombus or a Square.
The diagonals of a square are equal. The diagonals of a rhombus are unequal. Compute the lengths of the two diagonals AC and BD.
The length of AC is √162 and the length of BD is √2.
As the diagonals are not equal and the sides are equal, the given quadrilateral is a Rhombus.
Hence, the given quadrilateral is either a Rhombus or a Square.
The diagonals of a square are equal. The diagonals of a rhombus are unequal. Compute the lengths of the two diagonals AC and BD.
The length of AC is √162 and the length of BD is √2.
As the diagonals are not equal and the sides are equal, the given quadrilateral is a Rhombus.
Most Upvoted Answer
Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5...
Solution:
To determine the shape of the quadrilateral, we need to analyze the properties of the sides and angles of the given coordinates.
1. Square: A square is a four-sided polygon with all sides equal in length and all angles equal to 90 degrees. The given coordinates do not have all sides equal to each other, so it cannot be a square.
2. Rectangle but not a square: A rectangle is a four-sided polygon with opposite sides equal in length and all angles equal to 90 degrees. The given coordinates do not have opposite sides equal in length, so it cannot be a rectangle.
3. Rhombus: A rhombus is a four-sided polygon with all sides equal in length. The given coordinates have sides AB and CD equal in length (AB = CD = √41) and sides BC and AD equal in length (BC = AD = √17). So, the quadrilateral ABCD is a rhombus.
4. Parallelogram but not a rhombus: A parallelogram is a four-sided polygon with opposite sides parallel to each other. The given coordinates do not have opposite sides parallel to each other, so it cannot be a parallelogram.
5. Kite: A kite is a four-sided polygon with two pairs of adjacent sides equal in length. The given coordinates do not have two pairs of adjacent sides equal in length, so it cannot be a kite.
Therefore, the shape of the given quadrilateral ABCD is a rhombus.
To determine the shape of the quadrilateral, we need to analyze the properties of the sides and angles of the given coordinates.
1. Square: A square is a four-sided polygon with all sides equal in length and all angles equal to 90 degrees. The given coordinates do not have all sides equal to each other, so it cannot be a square.
2. Rectangle but not a square: A rectangle is a four-sided polygon with opposite sides equal in length and all angles equal to 90 degrees. The given coordinates do not have opposite sides equal in length, so it cannot be a rectangle.
3. Rhombus: A rhombus is a four-sided polygon with all sides equal in length. The given coordinates have sides AB and CD equal in length (AB = CD = √41) and sides BC and AD equal in length (BC = AD = √17). So, the quadrilateral ABCD is a rhombus.
4. Parallelogram but not a rhombus: A parallelogram is a four-sided polygon with opposite sides parallel to each other. The given coordinates do not have opposite sides parallel to each other, so it cannot be a parallelogram.
5. Kite: A kite is a four-sided polygon with two pairs of adjacent sides equal in length. The given coordinates do not have two pairs of adjacent sides equal in length, so it cannot be a kite.
Therefore, the shape of the given quadrilateral ABCD is a rhombus.
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Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5, 4). What is the shape of the quadrilaterala)Squareb)Rectangle but not a squarec)Rhombusd)Parallelogram but not a rhombuse)KiteCorrect answer is option 'C'. Can you explain this answer?
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Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5, 4). What is the shape of the quadrilaterala)Squareb)Rectangle but not a squarec)Rhombusd)Parallelogram but not a rhombuse)KiteCorrect answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5, 4). What is the shape of the quadrilaterala)Squareb)Rectangle but not a squarec)Rhombusd)Parallelogram but not a rhombuse)KiteCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5, 4). What is the shape of the quadrilaterala)Squareb)Rectangle but not a squarec)Rhombusd)Parallelogram but not a rhombuse)KiteCorrect answer is option 'C'. Can you explain this answer?.
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