What are the coordinates of the centroid of a triangle with vertices A(−6, 0) , B(−4, 4) , and C(0, 2) ? Enter your answers in the boxes.

Answer:The coordinates of the centroid of the triangle is (-3.33 , 2)Step-by-step explanation:Given:Coordinated if the vertices of the triangle = A(−6, 0) , B(−4, 4) , C(0, 2) To Find: Coordinates of the centroid of a triangle = ?Solution:Let the coordinate of the centroid be [tex]O_x[/tex] and [tex]O_y[/tex]when the coordinates  of the  vertices of the triangle are given , the The coordinates of the  centroid is given by,[tex]O_x = \frac{A_x +B_x+C_x}{3}[/tex]        [tex]O_y = \frac{A_y +B_y+C_y}{3}[/tex]here[tex]A_x[/tex] = -6[tex]B_x[/tex] = -4[tex]C_x[/tex] = 0[tex]A_y[/tex] =0[tex]B_y[/tex] = 4[tex]C_y[/tex] = 2Substituting the values[tex]O_x = \frac{(-6)+(-4)+0}{3}[/tex]        [tex]O_y = \frac{0+4+2}{3}[/tex][tex]O_x = \frac{(-10)}{3}[/tex]                  [tex]O_y = \frac{6}{3}[/tex][tex]O_x = -3.33[/tex]                              [tex]O_y = 2[/tex]