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Two vertices of a triangle ABC are given by A (1,2) and B ( 3,5 ) and its centroid is G ( 3,4 ). find the coordinates of the third vertex C of the triangle ABC.
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Two vertices of a triangle ABC are given by A (1,2) and B ( 3,5 ) and...
Centroid, G=(x1+x2+x3/3,y1+y2+y3/3)
Let coordinates of third point be (x,y)
Placing the values, we get:
3=(1+3+x)/3
=>9=x+4
=>x=5
4=(2+5+y)/3
=>12=y+7
=>y=5
Therefore, coordinates of the third point is (5,5)
Let coordinates of third point be (x,y)
Placing the values, we get:
3=(1+3+x)/3
=>9=x+4
=>x=5
4=(2+5+y)/3
=>12=y+7
=>y=5
Therefore, coordinates of the third point is (5,5)
Community Answer
Two vertices of a triangle ABC are given by A (1,2) and B ( 3,5 ) and...
Given:
Two vertices of the triangle ABC are A(1,2) and B(3,5) and the centroid is G(3,4).
To find:
The coordinates of the third vertex C of the triangle ABC.
Approach:
We know that the centroid of a triangle divides each median into two parts, where the ratio of the lengths of the two parts is 2:1. Using this concept, we can find the coordinates of the third vertex C.
Step 1: Finding the coordinates of the centroid G:
The centroid G divides the line segment joining the vertices A and B in the ratio 2:1. Let's calculate the coordinates of G using the formula:
G = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3)
Substituting the given values:
3 = ((1 + 3 + x3)/3) (x-coordinate)
4 = ((2 + 5 + y3)/3) (y-coordinate)
Simplifying the equations:
9 = 1 + 3 + x3 (multiplying both sides by 3)
12 = 2 + 5 + y3 (multiplying both sides by 3)
Solving the equations, we find:
x3 = 5 (subtracting 4 from both sides of the first equation)
y3 = 2 (subtracting 5 from both sides of the second equation)
Step 2: Finding the coordinates of the third vertex C:
We now have the coordinates of G as (3,4) and the third vertex C as (x3, y3) = (5,2).
Hence, the coordinates of the third vertex C of the triangle ABC are (5,2).
Two vertices of the triangle ABC are A(1,2) and B(3,5) and the centroid is G(3,4).
To find:
The coordinates of the third vertex C of the triangle ABC.
Approach:
We know that the centroid of a triangle divides each median into two parts, where the ratio of the lengths of the two parts is 2:1. Using this concept, we can find the coordinates of the third vertex C.
Step 1: Finding the coordinates of the centroid G:
The centroid G divides the line segment joining the vertices A and B in the ratio 2:1. Let's calculate the coordinates of G using the formula:
G = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3)
Substituting the given values:
3 = ((1 + 3 + x3)/3) (x-coordinate)
4 = ((2 + 5 + y3)/3) (y-coordinate)
Simplifying the equations:
9 = 1 + 3 + x3 (multiplying both sides by 3)
12 = 2 + 5 + y3 (multiplying both sides by 3)
Solving the equations, we find:
x3 = 5 (subtracting 4 from both sides of the first equation)
y3 = 2 (subtracting 5 from both sides of the second equation)
Step 2: Finding the coordinates of the third vertex C:
We now have the coordinates of G as (3,4) and the third vertex C as (x3, y3) = (5,2).
Hence, the coordinates of the third vertex C of the triangle ABC are (5,2).
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Two vertices of a triangle ABC are given by A (1,2) and B ( 3,5 ) and its centroid is G ( 3,4 ). find the coordinates of the third vertex C of the triangle ABC.
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Two vertices of a triangle ABC are given by A (1,2) and B ( 3,5 ) and its centroid is G ( 3,4 ). find the coordinates of the third vertex C of the triangle ABC. for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Two vertices of a triangle ABC are given by A (1,2) and B ( 3,5 ) and its centroid is G ( 3,4 ). find the coordinates of the third vertex C of the triangle ABC. covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two vertices of a triangle ABC are given by A (1,2) and B ( 3,5 ) and its centroid is G ( 3,4 ). find the coordinates of the third vertex C of the triangle ABC. .
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