Question

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 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} A(-6,0)\quad B(-4,4)\quad C(0,2)\\ \quad \\ \left(\cfrac{-6-4+0}{3}\quad ,\cfrac{0+4+2}{3}\quad \right) \end{array}`

Answer 2

Centroid of a Triangle states that the centre of the triangle that can be calculated as the point of intersection of all the three medians of a triangle, and this median is a line drawn from the midpoint of a side to the opposite vertex.

The coordinates of the centroid are simply the average of the coordinates of the vertices of triangle ABC.

The Centroid formula is,

`C = {(x_(1)+x_(2)+x_(3))/(3) , (y_(1)+y_(2)+y_(3))/(3)` where C is the centroid of the triangle ;
`x_(1),x_(2),x_(3)` are the x-coordinates of the vertices of the triangle and
`y_(1),y_(2),y_(3)` are the y-coordinates of the vertices of the triangle.

Given the vertices of triangle A(
`x_(1),y_(1)`)= (-6,0) , B(
`x_(2),y_(2)`)= (-4, 4) and C(
`x_(3),y_(3)`)=(0,2)

then,

the centroid of triangle C is,

`\{(-6+(-4)+0)/(3) , (0+4+2)/(3)\}` =
`\{(-6-4+0)/(3) , (6)/(3)\}=\{(-10)/(3) , 2\}`