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The points (1, 1), (–1, 5), (7, 9) and (9, 5) taken in such order that it will form a
- a)Rectangle
- b)Square
- c)Rhombus
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The points (1, 1), (–1, 5), (7, 9) and (9, 5) taken in such orde...
Let the points be A(1, 1), B(–1, 5), C(7, 9) and D(9, 5)
Now, by using distance formula, we get
AB = CD, BC = DA and AC = BD
∴ ABCD forms a rectangle.
Now, by using distance formula, we get
AB = CD, BC = DA and AC = BD
∴ ABCD forms a rectangle.
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Community Answer
The points (1, 1), (–1, 5), (7, 9) and (9, 5) taken in such orde...
Understanding the Points
The points given are (1, 1), (–1, 5), (7, 9), and (9, 5). To determine the shape they form, we need to analyze their positions on the coordinate plane.
Plotting the Points
- Point A (1, 1): This point is in the first quadrant.
- Point B (–1, 5): This point is in the second quadrant.
- Point C (7, 9): This point is in the first quadrant.
- Point D (9, 5): This point is in the first quadrant.
Calculating Distances
To determine if these points form a rectangle, we need to check the lengths of the sides and the diagonals.
- Distance AB: From (1, 1) to (–1, 5) is calculated as √[(–1-1)² + (5-1)²] = √[4 + 16] = √20.
- Distance BC: From (–1, 5) to (7, 9) is √[(7+1)² + (9-5)²] = √[64 + 16] = √80.
- Distance CD: From (7, 9) to (9, 5) is √[(9-7)² + (5-9)²] = √[4 + 16] = √20.
- Distance DA: From (9, 5) to (1, 1) is √[(1-9)² + (1-5)²] = √[64 + 16] = √80.
Checking for Right Angles
To confirm it's a rectangle, we need to verify if adjacent sides are perpendicular. The slopes of the lines can be used for this:
- Slope AB & Slope BC: They yield negative reciprocals, confirming a right angle.
Conclusion
Since the opposite sides are equal and the angles formed are right angles, the points (1, 1), (–1, 5), (7, 9), and (9, 5) indeed form a rectangle. Thus, the correct answer is option 'A'.
The points given are (1, 1), (–1, 5), (7, 9), and (9, 5). To determine the shape they form, we need to analyze their positions on the coordinate plane.
Plotting the Points
- Point A (1, 1): This point is in the first quadrant.
- Point B (–1, 5): This point is in the second quadrant.
- Point C (7, 9): This point is in the first quadrant.
- Point D (9, 5): This point is in the first quadrant.
Calculating Distances
To determine if these points form a rectangle, we need to check the lengths of the sides and the diagonals.
- Distance AB: From (1, 1) to (–1, 5) is calculated as √[(–1-1)² + (5-1)²] = √[4 + 16] = √20.
- Distance BC: From (–1, 5) to (7, 9) is √[(7+1)² + (9-5)²] = √[64 + 16] = √80.
- Distance CD: From (7, 9) to (9, 5) is √[(9-7)² + (5-9)²] = √[4 + 16] = √20.
- Distance DA: From (9, 5) to (1, 1) is √[(1-9)² + (1-5)²] = √[64 + 16] = √80.
Checking for Right Angles
To confirm it's a rectangle, we need to verify if adjacent sides are perpendicular. The slopes of the lines can be used for this:
- Slope AB & Slope BC: They yield negative reciprocals, confirming a right angle.
Conclusion
Since the opposite sides are equal and the angles formed are right angles, the points (1, 1), (–1, 5), (7, 9), and (9, 5) indeed form a rectangle. Thus, the correct answer is option 'A'.
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The points (1, 1), (–1, 5), (7, 9) and (9, 5) taken in such order that it will form aa)Rectangleb)Squarec)Rhombusd)None of theseCorrect 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, 1), (–1, 5), (7, 9) and (9, 5) taken in such order that it will form aa)Rectangleb)Squarec)Rhombusd)None of theseCorrect 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, 1), (–1, 5), (7, 9) and (9, 5) taken in such order that it will form aa)Rectangleb)Squarec)Rhombusd)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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