Question

What is the point of the centroid? A-(5,5) B-(1,7)C-(3,2)

Answer 1

The centroid of a triangle is the point where its three medians intersect, and it serves as the triangle's center of mass or balance point. The coordinates of the centroid can be calculated by averaging the coordinates of the triangle's vertices.

Given the vertices of the triangle A(5,5), B(1,7), and C(3,2), the formula for the centroid \((G_x, G_y)\) is:

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

Substituting the coordinates of points A, B, and C:

\[
G_x = \frac{5 + 1 + 3}{3} = \frac{9}{3} = 3
\]
\[
G_y = \frac{5 + 7 + 2}{3} = \frac{14}{3} \approx 4.67
\]

Thus, the coordinates of the centroid are approximately:

\[
G \left(3, \frac{14}{3}\right) \text{ or } G(3, 4.67)
\]

So the centroid of the triangle formed by the points A(5,5), B(1,7), and C(3,2) is \(G\left(3, \frac{14}{3}\right)\).