Grade 12th passAnalytical Geometry
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
1 Answer
Gopal Gopakumar
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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