Question

What are the coordinates of the centroid of a triangle with vertices P(−4, −1) , Q(2, 2) , and R(2, −3) ?

Enter your answers in the boxes.

Answer 1

`\bf \qquad \textit{Centroid of a Triangle} \\\\\\ \begin{array}{llll} A(x_1,y_1)\quad B(x_2,y_2)\quad C(x_3,y_3)\\ \quad \\ \left(\cfrac{x_1+x_2+x_3}{3}\quad ,\cfrac{y_1+y_2+y_3}{3}\quad \right) \end{array} \\\\ -------------------------------\\\\ \begin{array}{llll} P(-4,-1)\qquad Q(2,2)\qquad R(2,-3)\\ \quad \\ \left(\cfrac{-4+2+2}{3}\quad ,\cfrac{-1+2-3}{3}\quad \right) \end{array}`

Answer 2

`G(x,y)=(0;-0.67)`

Explanation:

The centroid of a triangle can be calculated with this formula:

`G(x,y)=((x_(1)+x_(2)+x_(3))/(3); (y_(1)+y_(2)+y_(3))/(3))`

The centroid is the average point among the three vertex of a triangle, it's a point formed by the triple interception of all medians of a triangle, the centroid is also called the barycenter or center of mass.

So, replacing all three points into the formula, we have:

`G(x,y)=((x_(1)+x_(2)+x_(3))/(3); (y_(1)+y_(2)+y_(3))/(3))\\G(x,y)=((-4+2+2)/(3); (-1+2+-3)/(3))\\G(x,y)=((0)/(3); (-2)/(3))\\G(x,y)=(0;-0.67)`

Therefore, the centroid is at
`G(x,y)=(0;-0.67)`