Class 10 Exam > Class 10 Questions > The points (3, 2), (0, 5), (-3, 2) and (0, -1...
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The points (3, 2), (0, 5), (-3, 2) and (0, -1) are the vertices of a quadrilateral. Which quadrilateral is it?
- a)Rectangle
- b)Square
- c)Parallelogram
- d)Rhombus
Correct answer is option 'B'. Can you explain this answer?
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The points (3, 2), (0, 5), (-3, 2) and (0, -1) are the vertices of a q...
Vertices of the Quadrilateral
- (3, 2)
- (0, 5)
- (-3, 2)
- (0, -1)
Explanation
To determine the type of quadrilateral formed by these vertices, we need to examine the properties of different quadrilaterals.
Square
A square is a special type of rectangle with all four sides of equal length and all angles of 90 degrees.
Analysis
- Calculate the distance between each pair of vertices using the distance formula: √[(x2 - x1)^2 + (y2 - y1)^2]
- Calculate the slopes of the lines passing through each pair of vertices to check for perpendicularity (for right angles).
Conclusion
After calculating the distances and slopes, we find that the given vertices form a quadrilateral with sides of equal length and right angles at each vertex. Therefore, the quadrilateral formed by the given vertices is a square.
- (3, 2)
- (0, 5)
- (-3, 2)
- (0, -1)
Explanation
To determine the type of quadrilateral formed by these vertices, we need to examine the properties of different quadrilaterals.
Square
A square is a special type of rectangle with all four sides of equal length and all angles of 90 degrees.
Analysis
- Calculate the distance between each pair of vertices using the distance formula: √[(x2 - x1)^2 + (y2 - y1)^2]
- Calculate the slopes of the lines passing through each pair of vertices to check for perpendicularity (for right angles).
Conclusion
After calculating the distances and slopes, we find that the given vertices form a quadrilateral with sides of equal length and right angles at each vertex. Therefore, the quadrilateral formed by the given vertices is a square.
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The points (3, 2), (0, 5), (-3, 2) and (0, -1) are the vertices of a quadrilateral. Which quadrilateral is it?a)Rectangleb)Squarec)Parallelogramd)RhombusCorrect answer is option 'B'. Can you explain this answer?
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