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.

Question 1184205: 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.
Answer by ikleyn(52799) (Show Source): You can put this solution on YOUR website!
.
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

Solved and explained.

RELATED QUESTIONS
3. Triangle PQR has vertices P(1,4), Q(-5,2) and R(-1,-4). The coordinates of the... (answered by ikleyn)

The vertices of a triangle are P (-1,-1) Q(2,1) and R (3,-1). Find the equation of the... (answered by checkley71)

The points P(−3,�6) and Q(1,�4) are two vertices of right... (answered by josgarithmetic,MathTherapy,ikleyn)

The vertices of triangle PQR are P(1,3),Q(5,4) and R(5,15).find a)the length of PR b)the... (answered by josgarithmetic)

A line with slope equal to 1 and a line with slope equal to 2 intersect at the point... (answered by mananth)

The vertices PQR are located at P -5, 2 and Q -2,5 and R -1, -1. The triangle can be... (answered by rothauserc)

If P(0, 5), Q(4,4) and R(3, 8) are the vertices of a triangle PQR, find the tangent of... (answered by ikleyn)

find the perimeter of the polygon PQR with it vertices at P(-4, 1), Q(2, 1), and R(0,... (answered by josgarithmetic)