Question

Find the coordinates of the centroid of the triangle

with the given vertices.
X(6, 0), Y(2, 8), Z(-2,-2)
Centroid at___

Answer 1

The coordinates of the centroid are (2, 2).

Step-by-step explanation:

The coordinates of the centroid of a triangle can be found by taking the average of the x-coordinates and the average of the y-coordinates of the vertices.

To find the centroid of a triangle with given vertices, you need to find the average of the x-coordinates and the average of the y-coordinates of the vertices.

For the given triangle with vertices X(6, 0), Y(2, 8), and Z(-2, -2),

X-coordinate of centroid: (6 + 2 - 2) / 3 = 2

Y-coordinate of centroid: (0 + 8 - 2) / 3 = 2

Therefore, the coordinates of the centroid are (2, 2).

Answer 2

`\qquad \textit{Centroid of a Triangle} \\\\ \left(\cfrac{x_1+x_2+x_3}{3}~~,\cfrac{y_1+y_2+y_3}{3}~~ \right)\quad \begin{cases} X(\stackrel{x_1}{6},\stackrel{y_1}{0})\\ Y(\stackrel{x_2}{2},\stackrel{y_2}{8})\\ Z(\stackrel{x_3}{-2},\stackrel{y_3}{-2}) \end{cases} \\\\\\ \left( \cfrac{6+2-2}{3}~~,~~\cfrac{0+8-2}{3} \right)\implies \left(\cfrac{6}{3}~~,~~ \cfrac{6}{3} \right)\implies \text{\LARGE (2~~,~~2)}`