Question

(-3, -1)
(2, -1)
(2, 3)

When the three medians of the triangle are drawn, they meet at single point. What is the point of the centroid? Leave all the results in fractions

centroid ( _, _)

Answer 1

To find the centroid of a triangle defined by the vertices \((-3, -1)\), \((2, -1)\), and \((2, 3)\), we use the formula for the centroid \((G_x, G_y)\):

\[
G_x = \frac{x_1 + x_2 + x_3}{3}, \quad G_y = \frac{y_1 + y_2 + y_3}{3}
\]

Where:
- \((x_1, y_1) = (-3, -1)\)
- \((x_2, y_2) = (2, -1)\)
- \((x_3, y_3) = (2, 3)\)

Now we can calculate \(G_x\) and \(G_y\):

First, we calculate \(G_x\):

\[
G_x = \frac{-3 + 2 + 2}{3} = \frac{1}{3}
\]

Next, we calculate \(G_y\):

\[
G_y = \frac{-1 + (-1) + 3}{3} = \frac{1}{3}
\]

Thus, the coordinates of the centroid are:

\[
\text{centroid} \left( \frac{1}{3}, \frac{1}{3} \right)
\]

Final answer:

\(\text{centroid} \left( \frac{1}{3}, \frac{1}{3} \right)\)