Equation of Locus of a point

Question

For the variable triangle $ABC$ with the fixed vertex at $C(1,2)$ and $A,B$ having co ordinates $(\cos t, \sin t)$, $(\sin t, -\cos t)$ respectively, find the locus of its centroid.

Plz help me, I could not even get how to start.

Answer 1

HINT:

I would say, coordinates of the centroid of the triangle:

$x_{ce}=\frac{x_A+x_B+x_C}{3},\quad y_{ce}=\frac{y_A+y_B+y_C}{3}$

Answer 2

Hint:

Use the fact that, for triangle, of vertices $A=(x_A,y_A)$, $B=(x_B,y_B)$, $C=(x_C,y_C)$, the centroid $M$ has coordinates: $$ (x_M,y,M)=\left(\frac{x_A+x_B+x_C}{3},\frac{y_A+y_B+y_C}{3} \right) $$