Question

What is the centroid of the triangle
coordinates of each point are
A(5,5), B(1,7), C(3,2)

Answer 1

The centroid of a triangle can be found using the formula for the coordinates of the centroid \( G \):

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

Given the coordinates of the triangle vertices:
- \( A(5, 5) \)
- \( B(1, 7) \)
- \( C(3, 2) \)

We can substitute the coordinates into the formula:

1. Calculate the x-coordinate of the centroid:
\[
x = \frac{5 + 1 + 3}{3} = \frac{9}{3} = 3
\]

2. Calculate the y-coordinate of the centroid:
\[
y = \frac{5 + 7 + 2}{3} = \frac{14}{3} \approx 4.67
\]

So, the centroid \( G \) of the triangle formed by points A, B, and C is:

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