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A quadrilateral is formed by pairs of lines xy+x+y+1=0, xy+3x+3y+9=0, then quadrilateral is
- a)a parallelogram
- b)a rhombus
- c)a rectangle
- d)a square
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A quadrilateral is formed by pairs of lines xy+x+y+1=0, xy+3x+3y+9=0, ...
Given Quadrilateral Equations:
- Equation 1: xy + x + y + 1 = 0
- Equation 2: xy + 3x + 3y + 9 = 0
Explanation:
1. Properties of Quadrilaterals:
Quadrilaterals have different properties based on their sides and angles. Some common types of quadrilaterals are parallelograms, rhombuses, rectangles, and squares.
2. Analyzing the Equations:
To determine the type of quadrilateral formed by the given equations, we need to analyze their properties. By rearranging the equations, we can identify the slopes and intercepts of the lines.
3. Identifying the Quadrilateral:
- Upon analyzing the given equations, we find that they represent the equations of two pairs of parallel lines.
- When two pairs of parallel lines are formed, a quadrilateral is created.
- The properties of the quadrilateral can be determined by examining the slopes and intercepts of the lines.
4. Conclusion - Quadrilateral Type:
- The given equations form a square when analyzed based on their slopes and intercepts.
- A square is a special type of quadrilateral that has all four sides equal in length and all interior angles measuring 90 degrees.
- Therefore, the quadrilateral formed by the given equations is a square.
Therefore, the correct answer is option 'd) a square'.
- Equation 1: xy + x + y + 1 = 0
- Equation 2: xy + 3x + 3y + 9 = 0
Explanation:
1. Properties of Quadrilaterals:
Quadrilaterals have different properties based on their sides and angles. Some common types of quadrilaterals are parallelograms, rhombuses, rectangles, and squares.
2. Analyzing the Equations:
To determine the type of quadrilateral formed by the given equations, we need to analyze their properties. By rearranging the equations, we can identify the slopes and intercepts of the lines.
3. Identifying the Quadrilateral:
- Upon analyzing the given equations, we find that they represent the equations of two pairs of parallel lines.
- When two pairs of parallel lines are formed, a quadrilateral is created.
- The properties of the quadrilateral can be determined by examining the slopes and intercepts of the lines.
4. Conclusion - Quadrilateral Type:
- The given equations form a square when analyzed based on their slopes and intercepts.
- A square is a special type of quadrilateral that has all four sides equal in length and all interior angles measuring 90 degrees.
- Therefore, the quadrilateral formed by the given equations is a square.
Therefore, the correct answer is option 'd) a square'.
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A quadrilateral is formed by pairs of lines xy+x+y+1=0, xy+3x+3y+9=0, then quadrilateral isa)a parallelogramb)a rhombusc)a rectangled)a squareCorrect answer is option 'D'. Can you explain this answer?
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