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For the variable triangle ABC with fixed vertex C(1,2) and A,B having coordinates(cost,sint),(sint,-cost),find the locus of the centroid.

For the variable triangle ABC with fixed vertex C(1,2) and A,B having coordinates(cost,sint),(sint,-cost),find the locus of the centroid.

Grade:11

1 Answers

vikas askiitian expert
509 Points
12 years ago

centroid of triangle  = [ x1+x2+x3/3 , y1+y2+y3/3 ]

centroid = [ (1+cost+sint)/3 , (2+sint -cost)/3 ] = (x,y)             ..................1

from eq 1

3x = 1 + cost + sint 

(3x-1) = sint + cost           ..................2

3y = 2 + sint - cost      

(3y-2) = sint - cost           ............... 3

now applying , (eq 2)2  + (eq3 )2

(3x-1)2 + (3y-2)2  = 2

this is equation of circle

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