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If A(2,-3) and B(-2,1) are two vertices of a triangle and the third vertex moves on the line 2x+3y=9 then the locus of the centroid of the triangle is?

If A(2,-3) and B(-2,1) are two vertices of a triangle and the third vertex moves on the line 2x+3y=9 then the locus of the centroid of the triangle is?

Grade:11

3 Answers

Vikas TU
14149 Points
4 years ago
Let the coordinates of centroid be (h,k)
h = (2 – 2 + x)/3
k= ( - 3+ 1 + y )/3
Where (x,y) are any point on the line 2x+3y=9
3h = x     and   9k + 2 = y
Now (x,y) satisfy the point on the line 2x+3y=9
2 ( 3h ) + 3 ( 9k + 2 ) = 9
  • 2h + 3k = 1
So the locus is 2x + 3 y =1.
sarthak
13 Points
2 years ago
Let A(-3,2) and (-2,1) be the vertices  of a trriengle ABC If the centroid of this triangle lies on the line 3x+4y+2=o then the vertex C lies on the line
ankit singh
askIITians Faculty 614 Points
11 months ago
 
Let the coordinates of centroid be (h,k)
h = (2 – 2 + x)/3
k= ( - 3+ 1 + y )/3
Where (x,y) are any point on the line 2x+3y=9
3h = x     and   9k + 2 = y
Now (x,y) satisfy the point on the line 2x+3y=9
2 ( 3h ) + 3 ( 9k + 2 ) = 9
  • 2h + 3k = 1
So the locus is 2x + 3 y =1.

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