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
sanjeev , 9 Years ago
Grade 12th pass
Analytical Geometry> find the locus of centroid of tirangle if...
1 AnswersGopal 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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