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Let C be the centroid of the triangle with vertices (3, -1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y - 1 = 0 and 3x - y + 1 = 0. Then the line passing through the points C and P also passes through the point
- a)(-9, -6)
- b)(-9, -7)
- c)(9, 7)
- d)(7, 6)
Correct answer is option 'A'. Can you explain this answer?
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Let C be the centroid of the triangle with vertices (3, -1), (1, 3) an...
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Let C be the centroid of the triangle with vertices (3, -1), (1, 3) an...
Given Information:
We are given the vertices of a triangle, and we need to find the equation of the line passing through the centroid of the triangle and the point of intersection of two given lines.
Step-by-Step Solution:
1. Finding the Centroid:
The centroid of a triangle can be found by taking the average of the x-coordinates and the average of the y-coordinates of its three vertices. Let's find the coordinates of the centroid C using this formula.
Given vertices of the triangle:
A(3, -1), B(1, 3), C(2, 4)
The x-coordinate of the centroid C is given by:
x-coordinate of C = (x-coordinate of A + x-coordinate of B + x-coordinate of C)/3
= (3 + 1 + 2)/3
= 6/3
= 2
The y-coordinate of the centroid C is given by:
y-coordinate of C = (y-coordinate of A + y-coordinate of B + y-coordinate of C)/3
= (-1 + 3 + 4)/3
= 6/3
= 2
So the centroid C is located at (2, 2).
2. Finding the Point of Intersection:
We are given two lines:
Line 1: x - 3y - 1 = 0
Line 2: 3x - y - 1 = 0
We need to find the point of intersection P of these two lines. We can solve these two equations simultaneously to find the coordinates of P.
Let's solve the equations:
From Line 1, we get:
x - 3y - 1 = 0
x = 3y + 1
Substituting this value of x in Line 2, we get:
3(3y + 1) - y - 1 = 0
9y + 3 - y - 1 = 0
8y + 2 = 0
8y = -2
y = -2/8
y = -1/4
Substituting this value of y in Line 1, we get:
x = 3(-1/4) + 1
x = -3/4 + 1
x = 1/4
So the point of intersection P is located at (1/4, -1/4).
3. Finding the Equation of the Line passing through C and P:
We have the coordinates of the centroid C and the point of intersection P. We can use these two points to find the equation of the line passing through them.
Let's find the slope of the line passing through C and P:
Slope = (y-coordinate of P - y-coordinate of C) / (x-coordinate of P - x-coordinate of C)
= (-1/4 - 2) / (1/4 - 2)
= (-9/4) / (-7/4)
= 9/7
Now we have the slope and one point (C) on the line. We can use the point-slope form of a linear equation to find the equation of the line passing through C and P.
Using the point-slope form, we have:
y - y-coordinate
We are given the vertices of a triangle, and we need to find the equation of the line passing through the centroid of the triangle and the point of intersection of two given lines.
Step-by-Step Solution:
1. Finding the Centroid:
The centroid of a triangle can be found by taking the average of the x-coordinates and the average of the y-coordinates of its three vertices. Let's find the coordinates of the centroid C using this formula.
Given vertices of the triangle:
A(3, -1), B(1, 3), C(2, 4)
The x-coordinate of the centroid C is given by:
x-coordinate of C = (x-coordinate of A + x-coordinate of B + x-coordinate of C)/3
= (3 + 1 + 2)/3
= 6/3
= 2
The y-coordinate of the centroid C is given by:
y-coordinate of C = (y-coordinate of A + y-coordinate of B + y-coordinate of C)/3
= (-1 + 3 + 4)/3
= 6/3
= 2
So the centroid C is located at (2, 2).
2. Finding the Point of Intersection:
We are given two lines:
Line 1: x - 3y - 1 = 0
Line 2: 3x - y - 1 = 0
We need to find the point of intersection P of these two lines. We can solve these two equations simultaneously to find the coordinates of P.
Let's solve the equations:
From Line 1, we get:
x - 3y - 1 = 0
x = 3y + 1
Substituting this value of x in Line 2, we get:
3(3y + 1) - y - 1 = 0
9y + 3 - y - 1 = 0
8y + 2 = 0
8y = -2
y = -2/8
y = -1/4
Substituting this value of y in Line 1, we get:
x = 3(-1/4) + 1
x = -3/4 + 1
x = 1/4
So the point of intersection P is located at (1/4, -1/4).
3. Finding the Equation of the Line passing through C and P:
We have the coordinates of the centroid C and the point of intersection P. We can use these two points to find the equation of the line passing through them.
Let's find the slope of the line passing through C and P:
Slope = (y-coordinate of P - y-coordinate of C) / (x-coordinate of P - x-coordinate of C)
= (-1/4 - 2) / (1/4 - 2)
= (-9/4) / (-7/4)
= 9/7
Now we have the slope and one point (C) on the line. We can use the point-slope form of a linear equation to find the equation of the line passing through C and P.
Using the point-slope form, we have:
y - y-coordinate
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Let C be the centroid of the triangle with vertices (3, -1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y - 1 = 0 and 3x - y + 1 = 0. Then the line passing through the points C and P also passes through the pointa)(-9, -6)b)(-9, -7)c)(9, 7)d)(7, 6)Correct answer is option 'A'. Can you explain this answer?
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Let C be the centroid of the triangle with vertices (3, -1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y - 1 = 0 and 3x - y + 1 = 0. Then the line passing through the points C and P also passes through the pointa)(-9, -6)b)(-9, -7)c)(9, 7)d)(7, 6)Correct answer is option 'A'. 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 C be the centroid of the triangle with vertices (3, -1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y - 1 = 0 and 3x - y + 1 = 0. Then the line passing through the points C and P also passes through the pointa)(-9, -6)b)(-9, -7)c)(9, 7)d)(7, 6)Correct answer is option 'A'. 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 C be the centroid of the triangle with vertices (3, -1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y - 1 = 0 and 3x - y + 1 = 0. Then the line passing through the points C and P also passes through the pointa)(-9, -6)b)(-9, -7)c)(9, 7)d)(7, 6)Correct answer is option 'A'. Can you explain this answer?.
Let C be the centroid of the triangle with vertices (3, -1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y - 1 = 0 and 3x - y + 1 = 0. Then the line passing through the points C and P also passes through the pointa)(-9, -6)b)(-9, -7)c)(9, 7)d)(7, 6)Correct answer is option 'A'. 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 C be the centroid of the triangle with vertices (3, -1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y - 1 = 0 and 3x - y + 1 = 0. Then the line passing through the points C and P also passes through the pointa)(-9, -6)b)(-9, -7)c)(9, 7)d)(7, 6)Correct answer is option 'A'. 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 C be the centroid of the triangle with vertices (3, -1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y - 1 = 0 and 3x - y + 1 = 0. Then the line passing through the points C and P also passes through the pointa)(-9, -6)b)(-9, -7)c)(9, 7)d)(7, 6)Correct answer is option 'A'. Can you explain this answer?.
Solutions for Let C be the centroid of the triangle with vertices (3, -1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y - 1 = 0 and 3x - y + 1 = 0. Then the line passing through the points C and P also passes through the pointa)(-9, -6)b)(-9, -7)c)(9, 7)d)(7, 6)Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Let C be the centroid of the triangle with vertices (3, -1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y - 1 = 0 and 3x - y + 1 = 0. Then the line passing through the points C and P also passes through the pointa)(-9, -6)b)(-9, -7)c)(9, 7)d)(7, 6)Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Let C be the centroid of the triangle with vertices (3, -1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y - 1 = 0 and 3x - y + 1 = 0. Then the line passing through the points C and P also passes through the pointa)(-9, -6)b)(-9, -7)c)(9, 7)d)(7, 6)Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Let C be the centroid of the triangle with vertices (3, -1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y - 1 = 0 and 3x - y + 1 = 0. Then the line passing through the points C and P also passes through the pointa)(-9, -6)b)(-9, -7)c)(9, 7)d)(7, 6)Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Let C be the centroid of the triangle with vertices (3, -1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y - 1 = 0 and 3x - y + 1 = 0. Then the line passing through the points C and P also passes through the pointa)(-9, -6)b)(-9, -7)c)(9, 7)d)(7, 6)Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
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