i need help with a question ...
ΔPQR has vertices P(1, 3), Q(-1, 1), and R(5, 1). Determine the coordinates of the centroid of ΔABC.
What goes centroid mean and how do you solve it!
Centroid means center.
Triangle Centroid -- from Wolfram MathWorld
If you know the coordinates of the vertices then the coordinates of the centroid are calculated by a simple formula:
If $\displaystyle P(x_P, y_P)$, $\displaystyle Q(x_Q, y_Q)$ and $\displaystyle R(x_R, y_R)$ then the centroid
$\displaystyle C\left(\dfrac13(x_P + x_Q + x_R)\ ,\ \dfrac13(y_P + y_Q + y_R)\right)$
With your question: $\displaystyle C\left(\dfrac53\ ,\ \dfrac53 \right)$
There is no such thing as "the" center of a general triangle. A triangle has many different kinds of center just as a collection of numbers has many different kinds of average. There is a very extensive online encycolpedia about triangle centers here:
ENCYCLOPEDIA OF TRIANGLE CENTERS
The formulas it gives use either trilinear or barycentric coordinates which are both quite different from ordinary Cartesian coordinates.