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The orthocentre of the triangle whose vertices are (5, -2), (-1, 2) and (1, 4) is
- a)[(1/5), (14/5)]
- b)[(14/5), (1/5)]
- c)[(1/5), (1/5)]
- d)[(14/5), (14/5)]
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The orthocentre of the triangle whose vertices are (5, -2), (-1, 2) an...
Explanation:
1. Orthocentre of a Triangle:
The orthocentre of a triangle is the point where the three altitudes of the triangle intersect. An altitude is a line segment drawn from a vertex of the triangle perpendicular to the opposite side.
2. Finding Altitudes:
To find the altitudes, we need to find the slopes of the lines passing through each vertex and perpendicular to the opposite side. Then, using the slope-intercept form of a line, we can find the equations of these altitudes.
3. Calculating Slopes:
Given the vertices (5, -2), (-1, 2), and (1, 4), we can calculate the slopes of the lines passing through these points and perpendicular to the opposite sides.
4. Finding Equations of Altitudes:
Using the slopes and the point-slope form of a line, we can find the equations of the altitudes passing through each vertex.
5. Solving for Orthocentre:
The orthocentre is the point of intersection of the three altitudes. By solving the equations of the altitudes simultaneously, we can find the coordinates of the orthocentre.
Therefore, after performing the calculations, the coordinates of the orthocentre of the given triangle are [(1/5), (14/5)], which corresponds to option 'A'.
1. Orthocentre of a Triangle:
The orthocentre of a triangle is the point where the three altitudes of the triangle intersect. An altitude is a line segment drawn from a vertex of the triangle perpendicular to the opposite side.
2. Finding Altitudes:
To find the altitudes, we need to find the slopes of the lines passing through each vertex and perpendicular to the opposite side. Then, using the slope-intercept form of a line, we can find the equations of these altitudes.
3. Calculating Slopes:
Given the vertices (5, -2), (-1, 2), and (1, 4), we can calculate the slopes of the lines passing through these points and perpendicular to the opposite sides.
4. Finding Equations of Altitudes:
Using the slopes and the point-slope form of a line, we can find the equations of the altitudes passing through each vertex.
5. Solving for Orthocentre:
The orthocentre is the point of intersection of the three altitudes. By solving the equations of the altitudes simultaneously, we can find the coordinates of the orthocentre.
Therefore, after performing the calculations, the coordinates of the orthocentre of the given triangle are [(1/5), (14/5)], which corresponds to option 'A'.
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The orthocentre of the triangle whose vertices are (5, -2), (-1, 2) and (1, 4) isa)[(1/5), (14/5)]b)[(14/5), (1/5)]c)[(1/5), (1/5)]d)[(14/5), (14/5)]Correct answer is option 'A'. Can you explain this answer? for JEE 2026 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The orthocentre of the triangle whose vertices are (5, -2), (-1, 2) and (1, 4) isa)[(1/5), (14/5)]b)[(14/5), (1/5)]c)[(1/5), (1/5)]d)[(14/5), (14/5)]Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The orthocentre of the triangle whose vertices are (5, -2), (-1, 2) and (1, 4) isa)[(1/5), (14/5)]b)[(14/5), (1/5)]c)[(1/5), (1/5)]d)[(14/5), (14/5)]Correct answer is option 'A'. Can you explain this answer?.
The orthocentre of the triangle whose vertices are (5, -2), (-1, 2) and (1, 4) isa)[(1/5), (14/5)]b)[(14/5), (1/5)]c)[(1/5), (1/5)]d)[(14/5), (14/5)]Correct answer is option 'A'. Can you explain this answer? for JEE 2026 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The orthocentre of the triangle whose vertices are (5, -2), (-1, 2) and (1, 4) isa)[(1/5), (14/5)]b)[(14/5), (1/5)]c)[(1/5), (1/5)]d)[(14/5), (14/5)]Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The orthocentre of the triangle whose vertices are (5, -2), (-1, 2) and (1, 4) isa)[(1/5), (14/5)]b)[(14/5), (1/5)]c)[(1/5), (1/5)]d)[(14/5), (14/5)]Correct answer is option 'A'. Can you explain this answer?.
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