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find the locus of centroid of tirangle if two vertex are given and third vertex lies on the line

find the locus of centroid of tirangle if two vertex are given and third vertex lies on the line

Grade:12th pass

1 Answers

Gopal Gopakumar
27 Points
5 years ago
Let the given points be (A1,B1) , and (A2,B2) . Write the given line in the form of y = mx + c .
Hence, the third point becomes (x, mx + c) .
Putting in equation of centroid gives,
 
(A1 + A2 + x)/3 = h ( x – coordinate of locus)  
and  (B1 + B2 + mx + c)/3 = k ( y – cordinate of locus)
 
Rearranging the two equation gives you,
 
3h – A1 – A2 = x   and  (3k – B1 – B2 – c)/m = x
 
equating the two and putting h = x and k = y finally will give the required answer.

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