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let A(2,-3) and B(-2,1) be vertices of triangle ABC,if centroid of this triangle moves on the line 2x+3y=1 then the locus of the vertex C is

let A(2,-3) and B(-2,1) be vertices of triangle ABC,if centroid of this triangle moves on the line 2x+3y=1 then the locus of the vertex C is
 

Grade:10

1 Answers

Arun
25750 Points
5 years ago
Dear student
 
 
Let C(h,k)
To find the centroid, (x1 +x2 +x3/3, y1  + y2 +y3/3)
(2-2+h/3, -3+1+k/3)
(h/3, k-2/3)
When we replace these values in equation of centroid,
​2.h/3 + 3. (k-2)/3 = 1
2h+3k=9
Putting x as h and y as k,
2x+3y=9
 
Hope it helps
 
Regards
Arun (askIITians forum expert)

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