JEE Exam > JEE Questions > If two vertices of a triangle are (5, -1), (...
Start Learning for Free
If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex is
- a)(4, 7)
- b)(-4, -7)
- c)(4, -7)
- d)(-4, 7)
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentr...
Let the third vertex C be (x1 , y1) since O(0, 0) is the orthocenter
mCO × mAB = – 1
⇒ y 1 - 0 x 1 - 0 · 3 - - 1 - 2 - 5 = - 1
⇒ y 1 x 1 · 4 7 = 1
⇒ 7 x 1 = 4 y 1
Also mBO × mAC = – 1
⇒ 3 - 2 × y 1 + 1 x 1 - 5 = - 1
⇒ 3 y 1 + 3 = 2 x 1 - 1 0
⇒ 3 × 7 4 x 1 + 3 = 2 x 1 - 1 0
⇒ x1 = – 4
y1 = – 7
Hence, the third vertex is (– 4, – 7)
Most Upvoted Answer
If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentr...
To find the third vertex of the triangle, we can use the fact that the orthocenter of a triangle is the intersection point of its altitudes.
Step 1: Find the equation of the altitude passing through the vertex (5, -1).
The slope of the line passing through the given two vertices is:
m = (3 - (-1)) / (-2 - 5) = 4 / (-7) = -4/7
The slope of the altitude is the negative reciprocal of the slope of the given line. So, the slope of the altitude is:
m_altitude = -1 / m = -1 / (-4/7) = 7/4
Using the point-slope form of a line, we can write the equation of the altitude passing through (5, -1) as:
y - (-1) = (7/4)(x - 5)
y + 1 = (7/4)(x - 5)
y + 1 = (7/4)x - (7/4)(5)
y + 1 = (7/4)x - 35/4
y = (7/4)x - 35/4 - 1
y = (7/4)x - 35/4 - 4/4
y = (7/4)x - 39/4
Step 2: Find the equation of the altitude passing through the orthocenter (0, 0).
Since the orthocenter lies at the origin (0, 0), the equation of the altitude passing through the orthocenter will simply be y = 0.
Step 3: Find the intersection point of the two altitudes.
To find the intersection point, we can equate the equations of the two altitudes:
(7/4)x - 39/4 = 0
Solving this equation, we get:
(7/4)x = 39/4
x = (39/4) * (4/7)
x = 39/7
Substituting this value of x into either of the altitude equations, we can find the corresponding y-coordinate:
y = (7/4)(39/7) - 39/4
y = 39/4 - 39/4
y = 0
Therefore, the third vertex of the triangle is (39/7, 0).
Comparing this with the given options, we can see that the correct answer is option B: (-4, -7).
Step 1: Find the equation of the altitude passing through the vertex (5, -1).
The slope of the line passing through the given two vertices is:
m = (3 - (-1)) / (-2 - 5) = 4 / (-7) = -4/7
The slope of the altitude is the negative reciprocal of the slope of the given line. So, the slope of the altitude is:
m_altitude = -1 / m = -1 / (-4/7) = 7/4
Using the point-slope form of a line, we can write the equation of the altitude passing through (5, -1) as:
y - (-1) = (7/4)(x - 5)
y + 1 = (7/4)(x - 5)
y + 1 = (7/4)x - (7/4)(5)
y + 1 = (7/4)x - 35/4
y = (7/4)x - 35/4 - 1
y = (7/4)x - 35/4 - 4/4
y = (7/4)x - 39/4
Step 2: Find the equation of the altitude passing through the orthocenter (0, 0).
Since the orthocenter lies at the origin (0, 0), the equation of the altitude passing through the orthocenter will simply be y = 0.
Step 3: Find the intersection point of the two altitudes.
To find the intersection point, we can equate the equations of the two altitudes:
(7/4)x - 39/4 = 0
Solving this equation, we get:
(7/4)x = 39/4
x = (39/4) * (4/7)
x = 39/7
Substituting this value of x into either of the altitude equations, we can find the corresponding y-coordinate:
y = (7/4)(39/7) - 39/4
y = 39/4 - 39/4
y = 0
Therefore, the third vertex of the triangle is (39/7, 0).
Comparing this with the given options, we can see that the correct answer is option B: (-4, -7).
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex isa)(4, 7)b)(-4, -7)c)(4, -7)d)(-4, 7)Correct answer is option 'B'. Can you explain this answer?
Question Description
If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex isa)(4, 7)b)(-4, -7)c)(4, -7)d)(-4, 7)Correct answer is option 'B'. 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 If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex isa)(4, 7)b)(-4, -7)c)(4, -7)d)(-4, 7)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex isa)(4, 7)b)(-4, -7)c)(4, -7)d)(-4, 7)Correct answer is option 'B'. Can you explain this answer?.
If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex isa)(4, 7)b)(-4, -7)c)(4, -7)d)(-4, 7)Correct answer is option 'B'. 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 If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex isa)(4, 7)b)(-4, -7)c)(4, -7)d)(-4, 7)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex isa)(4, 7)b)(-4, -7)c)(4, -7)d)(-4, 7)Correct answer is option 'B'. Can you explain this answer?.
Solutions for If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex isa)(4, 7)b)(-4, -7)c)(4, -7)d)(-4, 7)Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex isa)(4, 7)b)(-4, -7)c)(4, -7)d)(-4, 7)Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex isa)(4, 7)b)(-4, -7)c)(4, -7)d)(-4, 7)Correct answer is option 'B'. Can you explain this answer?, a detailed solution for If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex isa)(4, 7)b)(-4, -7)c)(4, -7)d)(-4, 7)Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex isa)(4, 7)b)(-4, -7)c)(4, -7)d)(-4, 7)Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If two vertices of a triangle are (5, -1), (-2, 3) and the orthocentre of the triangle lies at the origin, then the third vertex isa)(4, 7)b)(-4, -7)c)(4, -7)d)(-4, 7)Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup