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Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 and 4x + 5y – 20 = 0. If the orthocentre of this triangle is at (1,1), then the equation of its third side is :
- a)122y – 26x – 1675 = 0
- b)26x + 61y + 1675 = 0
- c)122y + 26x + 1675 = 0
- d)26x – 122y – 1675 = 0
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 ...
Equation of AB is 3x – 2y + 6 = 0
equation of AC is 4x + 5y – 20 = 0
Equation of BE is 2x + 3y – 5 = 0
Equation of CF is 5x – 4y – 1 = 0
⇒ Equation of BC is 26x – 122y = 1675
Most Upvoted Answer
Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 ...
Understanding Triangle Properties
To find the equation of the third side of the triangle formed by the given lines and an orthocenter at (1,1), we follow these steps:
1. Identify the Lines
- The first line: 3x - 2y + 6 = 0
- The second line: 4x + 5y - 20 = 0
2. Find the Intersection Point
- We need to find the intersection of the two lines, which will be one vertex of the triangle.
3. Solve the System of Equations
- To find the point of intersection, solve the equations simultaneously.
- From the first line, express y in terms of x: y = (3/2)x + 3.
- Substitute this into the second line to find the value of x.
- Solve for both x and y to get the intersection point.
4. Calculate Slopes
- Determine the slopes of both lines:
- For line 1: slope = 3/2.
- For line 2: slope = -4/5.
5. Orthogonal Slopes
- The slope of the third side must be the negative reciprocal of the slopes of the other two lines to ensure that the orthocenter is at (1,1).
6. Equation of the Third Side
- Using the orthocenter (1,1), apply the slope found in the previous step to derive the equation of the third line using the point-slope form.
- Rearranging will lead to the final equation of the third side.
Conclusion
After performing these steps, you will arrive at the equation of the third side, which is represented as:
- 26x - 122y - 1675 = 0
This matches option 'D', confirming its correctness.
To find the equation of the third side of the triangle formed by the given lines and an orthocenter at (1,1), we follow these steps:
1. Identify the Lines
- The first line: 3x - 2y + 6 = 0
- The second line: 4x + 5y - 20 = 0
2. Find the Intersection Point
- We need to find the intersection of the two lines, which will be one vertex of the triangle.
3. Solve the System of Equations
- To find the point of intersection, solve the equations simultaneously.
- From the first line, express y in terms of x: y = (3/2)x + 3.
- Substitute this into the second line to find the value of x.
- Solve for both x and y to get the intersection point.
4. Calculate Slopes
- Determine the slopes of both lines:
- For line 1: slope = 3/2.
- For line 2: slope = -4/5.
5. Orthogonal Slopes
- The slope of the third side must be the negative reciprocal of the slopes of the other two lines to ensure that the orthocenter is at (1,1).
6. Equation of the Third Side
- Using the orthocenter (1,1), apply the slope found in the previous step to derive the equation of the third line using the point-slope form.
- Rearranging will lead to the final equation of the third side.
Conclusion
After performing these steps, you will arrive at the equation of the third side, which is represented as:
- 26x - 122y - 1675 = 0
This matches option 'D', confirming its correctness.
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Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 and 4x + 5y – 20 = 0. If the orthocentre of this triangle is at (1,1), then the equation of its third side is :a)122y – 26x – 1675 = 0b)26x + 61y + 1675 = 0c)122y + 26x + 1675 = 0d)26x – 122y – 1675 = 0Correct answer is option 'D'. Can you explain this answer?
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Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 and 4x + 5y – 20 = 0. If the orthocentre of this triangle is at (1,1), then the equation of its third side is :a)122y – 26x – 1675 = 0b)26x + 61y + 1675 = 0c)122y + 26x + 1675 = 0d)26x – 122y – 1675 = 0Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 and 4x + 5y – 20 = 0. If the orthocentre of this triangle is at (1,1), then the equation of its third side is :a)122y – 26x – 1675 = 0b)26x + 61y + 1675 = 0c)122y + 26x + 1675 = 0d)26x – 122y – 1675 = 0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 and 4x + 5y – 20 = 0. If the orthocentre of this triangle is at (1,1), then the equation of its third side is :a)122y – 26x – 1675 = 0b)26x + 61y + 1675 = 0c)122y + 26x + 1675 = 0d)26x – 122y – 1675 = 0Correct answer is option 'D'. Can you explain this answer?.
Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 and 4x + 5y – 20 = 0. If the orthocentre of this triangle is at (1,1), then the equation of its third side is :a)122y – 26x – 1675 = 0b)26x + 61y + 1675 = 0c)122y + 26x + 1675 = 0d)26x – 122y – 1675 = 0Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 and 4x + 5y – 20 = 0. If the orthocentre of this triangle is at (1,1), then the equation of its third side is :a)122y – 26x – 1675 = 0b)26x + 61y + 1675 = 0c)122y + 26x + 1675 = 0d)26x – 122y – 1675 = 0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 and 4x + 5y – 20 = 0. If the orthocentre of this triangle is at (1,1), then the equation of its third side is :a)122y – 26x – 1675 = 0b)26x + 61y + 1675 = 0c)122y + 26x + 1675 = 0d)26x – 122y – 1675 = 0Correct answer is option 'D'. Can you explain this answer?.
Solutions for Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 and 4x + 5y – 20 = 0. If the orthocentre of this triangle is at (1,1), then the equation of its third side is :a)122y – 26x – 1675 = 0b)26x + 61y + 1675 = 0c)122y + 26x + 1675 = 0d)26x – 122y – 1675 = 0Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 and 4x + 5y – 20 = 0. If the orthocentre of this triangle is at (1,1), then the equation of its third side is :a)122y – 26x – 1675 = 0b)26x + 61y + 1675 = 0c)122y + 26x + 1675 = 0d)26x – 122y – 1675 = 0Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 and 4x + 5y – 20 = 0. If the orthocentre of this triangle is at (1,1), then the equation of its third side is :a)122y – 26x – 1675 = 0b)26x + 61y + 1675 = 0c)122y + 26x + 1675 = 0d)26x – 122y – 1675 = 0Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 and 4x + 5y – 20 = 0. If the orthocentre of this triangle is at (1,1), then the equation of its third side is :a)122y – 26x – 1675 = 0b)26x + 61y + 1675 = 0c)122y + 26x + 1675 = 0d)26x – 122y – 1675 = 0Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 and 4x + 5y – 20 = 0. If the orthocentre of this triangle is at (1,1), then the equation of its third side is :a)122y – 26x – 1675 = 0b)26x + 61y + 1675 = 0c)122y + 26x + 1675 = 0d)26x – 122y – 1675 = 0Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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