Question

find the coordinates of the centroid of the triangle with the vertices $x(-3, 15)$, $y(1, 5)$, and $z(5, 10)$.

Explanation:

Step1: Recall centroid formula

The centroid $(G_x, G_y)$ of a triangle with vertices $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3)$ is given by:
$$G_x = \frac{x_1 + x_2 + x_3}{3}, \quad G_y = \frac{y_1 + y_2 + y_3}{3}$$

Step2: Substitute x-coordinates

Plug $x_1=-3$, $x_2=1$, $x_3=5$ into the x-formula:
$$G_x = \frac{-3 + 1 + 5}{3} = \frac{3}{3} = 1$$

Step3: Substitute y-coordinates

Plug $y_1=15$, $y_2=5$, $y_3=10$ into the y-formula:
$$G_y = \frac{15 + 5 + 10}{3} = \frac{30}{3} = 10$$

Answer:

$(1, 10)$