find the locus of centroid of tirangle if two vertex are given and third vertex lies on the line
sanjeev , 8 Years ago
Grade 12th pass
Analytical Geometry> find the locus of centroid of tirangle if...
1 AnswersGopal Gopakumar
Last Activity: 8 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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