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The points (-1, –2), (1, 0), (-1, 2), (-3, 0) form a quadrilateral of type:
- a)Square
- b)Rectangle
- c)Parallelogram
- d)Rhombus
Correct answer is option 'A'. Can you explain this answer?
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Understanding the Quadrilateral
The given points are (-1, -2), (1, 0), (-1, 2), and (-3, 0). To classify the quadrilateral formed by these points, we need to analyze the distances between the points and the angles formed.
Step 1: Distance Calculation
- Calculate the lengths of the sides:
- Distance between (-1, -2) and (1, 0):
- d1 = √[(1 - (-1))^2 + (0 - (-2))^2] = √[4 + 4] = √8 = 2√2
- Distance between (1, 0) and (-1, 2):
- d2 = √[(-1 - 1)^2 + (2 - 0)^2] = √[4 + 4] = √8 = 2√2
- Distance between (-1, 2) and (-3, 0):
- d3 = √[(-3 - (-1))^2 + (0 - 2)^2] = √[4 + 4] = √8 = 2√2
- Distance between (-3, 0) and (-1, -2):
- d4 = √[(-1 - (-3))^2 + (-2 - 0)^2] = √[4 + 4] = √8 = 2√2
Step 2: Analyzing Angles
- Check for right angles:
- The slopes of the sides can be calculated to confirm perpendicularity.
- The slopes between opposite sides will be negative reciprocals, confirming right angles.
Conclusion: Type of Quadrilateral
- All sides are equal (2√2), and each angle is 90 degrees.
- Thus, the quadrilateral formed is a Square.
Therefore, the correct answer is option A: Square.
The given points are (-1, -2), (1, 0), (-1, 2), and (-3, 0). To classify the quadrilateral formed by these points, we need to analyze the distances between the points and the angles formed.
Step 1: Distance Calculation
- Calculate the lengths of the sides:
- Distance between (-1, -2) and (1, 0):
- d1 = √[(1 - (-1))^2 + (0 - (-2))^2] = √[4 + 4] = √8 = 2√2
- Distance between (1, 0) and (-1, 2):
- d2 = √[(-1 - 1)^2 + (2 - 0)^2] = √[4 + 4] = √8 = 2√2
- Distance between (-1, 2) and (-3, 0):
- d3 = √[(-3 - (-1))^2 + (0 - 2)^2] = √[4 + 4] = √8 = 2√2
- Distance between (-3, 0) and (-1, -2):
- d4 = √[(-1 - (-3))^2 + (-2 - 0)^2] = √[4 + 4] = √8 = 2√2
Step 2: Analyzing Angles
- Check for right angles:
- The slopes of the sides can be calculated to confirm perpendicularity.
- The slopes between opposite sides will be negative reciprocals, confirming right angles.
Conclusion: Type of Quadrilateral
- All sides are equal (2√2), and each angle is 90 degrees.
- Thus, the quadrilateral formed is a Square.
Therefore, the correct answer is option A: Square.
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The points (-1, –2), (1, 0), (-1, 2), (-3, 0) form a quadrilateral of type:a)Squareb)Rectanglec)Parallelogramd)RhombusCorrect answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The points (-1, –2), (1, 0), (-1, 2), (-3, 0) form a quadrilateral of type:a)Squareb)Rectanglec)Parallelogramd)RhombusCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The points (-1, –2), (1, 0), (-1, 2), (-3, 0) form a quadrilateral of type:a)Squareb)Rectanglec)Parallelogramd)RhombusCorrect answer is option 'A'. Can you explain this answer?.
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