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= (,)

1 answer

The centroid of a triangle \( \triangle ABC \) is the point where the three medians intersect. It can be calculated using the coordinates of the vertices of the triangle.

If the vertices of the triangle \( A \), \( B \), and \( C \) are given by their coordinates:

  • \( A(x_1, y_1) \)
  • \( B(x_2, y_2) \)
  • \( C(x_3, y_3) \)

The coordinates of the centroid \( G \) of the triangle can be found using the formula: \[ G\left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) \]

So, the coordinates of the centroid \( G \) are: \[ G\left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) \]

Please provide the coordinates of the triangle's vertices, and we can calculate the specific coordinates of the centroid for you.