SOLUTION: Find the locus of R if points P(2, -3) and Q(-2, 1) are vertices of triangle PQR and centroid of PQR lies on line 2x + 3y = 1.

Let R = (x,y).


Then the centroid of the triangle PQR  has x-coordinate   = 1/3 of the sum x-coordinates of the vertices =  = .

                                           y-coordinate   = 1/3 of the sum y-coordinates of the vertices =  = .


We want the centroid points  (,) lie on the line  2x + 3y = 1.


So, we substitute    for    and    for    into this equation.  We get then

     +  = 1.


It is EQUIVALENT to 

     + (y-2) = 1,

    2x + 3*(y-2) = 3,

    2x + 3y - 6 = 3

    2x + 3y = 9.


Thus the locus of points R(x,y) is the straight line  2x + 3y = 9.    ANSWER