Question

if A(cosα ,sinα ), B(sinα,-cosα) C(1,2) are the vertices of a ΔABC ,then as α varies the locus of its centroid is ?

Answer 1

Step-by-step explanation:

A(cos a,sin a),B(sin a,-cos a)andC(1,2)

let the coordinates of the centroid G of triangle ABC (X,y) then

(X,y)=(cos a+sin a+1)/3,sin-cos a+2)/3)

=3x-1=cos a+sin a and 3y-2=sin a-cos a

squaring and adding we get

(3x^-1)^2+(3y-2)^2=cos^2a+sin^2a+2sin cosa

+sin^2a+cos^2a-2sin cosa

Ie(3x-1)^2+(3y-2)^2=2

ie9x^2+9y^2-12y+3=0 which is the locus

of the centroid