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.
Accepted Solution
A:
Answer: The centroid of the triangle PQR is [tex](0,\frac{-2}{3} )[/tex].Explanation:It is given that the vertices of the triangle are P(−4, −1) , Q(2, 2) , and R(2, −3).The formula to find the coordinates of the centroid of a triangle is,[tex]\text{coordinates of centroid}=(\frac{x_1+x_2+x_3}{3} ,\frac{y_1+y_2+y_3}{3} )[/tex]We have coordinates of all vertices, so we can directly substitute the values in the above mentioned formula.[tex]\text{coordinates of centroid}=(\frac{-4+2+2}{3} ,\frac{-1+2+(-3)}{3} )[/tex][tex]\text{coordinates of centroid}=(\frac{0}{3} ,\frac{-2}{3} )[/tex][tex]\text{coordinates of centroid}=(0,\frac{-2}{3} )[/tex]Therefore the coordinates of the centroid of a triangle PQR is [tex](0,\frac{-2}{3} )[/tex].