A scalene triangle made up of vertices upper A, upper B, and upper C, is plotted on a grid. Each of its vertices have their coordinates labeled, and they are connected to an interior point labeled upper D.

Question

The three medians of △ABC meet at a single point. What is the point of the centroid? Express all results in fractions.

(1 point)
centroid=(
,
)

Answer 1

To find the centroid of a triangle with vertices \( A(x_1, y_1) \), \( B(x_2, y_2) \), and \( C(x_3, y_3) \), we use the formula for the centroid \((G)\):

\[ G\left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) \]

You need to substitute the coordinates of vertices \( A \), \( B \), and \( C \) into this formula.

If you provide the coordinates of points \( A \), \( B \), and \( C \), I can help calculate the centroid. Please specify their coordinates.