Questions: Find the coordinates of the centroid of the triangle with the given vertices. A(-10,3), B(-4,5), C(-4,1)

Solution Steps

The centroid of a triangle with vertices \( A(x_1, y_1) \), \( B(x_2, y_2) \), and \( C(x_3, y_3) \) is given by: \[ \left( \frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3} \right) \]

Given the vertices: \[ A(-10, 3), \quad B(-4, 5), \quad C(-4, 1) \] Substitute the coordinates into the centroid formula: \[ \left( \frac{-10 + (-4) + (-4)}{3}, \frac{3 + 5 + 1}{3} \right) \]

Calculate the \( x \)-coordinate: \[ \frac{-10 - 4 - 4}{3} = \frac{-18}{3} = -6 \] Calculate the \( y \)-coordinate: \[ \frac{3 + 5 + 1}{3} = \frac{9}{3} = 3 \]

Final Answer