Question

A Triangle is drawn on a coordinate plane with vertices B (1,7), A( 5,5) and C (3,2).

When the three medians of the triangle are drawn, they meet at a single point. What is the point of the centroid?
(1 point)

Answer 1

To find the centroid of a triangle with vertices at points \( A(5, 5) \), \( B(1, 7) \), and \( C(3, 2) \), we can use the formula for the coordinates of the centroid \( G \):

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

where \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \) are the coordinates of the vertices.

Substituting the coordinates of the vertices:

- \( A(5, 5) \): \( x_1 = 5 \), \( y_1 = 5 \)
- \( B(1, 7) \): \( x_2 = 1 \), \( y_2 = 7 \)
- \( C(3, 2) \): \( x_3 = 3 \), \( y_3 = 2 \)

Now, calculate the coordinates of the centroid:

\[
G_x = \frac{5 + 1 + 3}{3} = \frac{9}{3} = 3
\]

\[
G_y = \frac{5 + 7 + 2}{3} = \frac{14}{3}
\]

Thus, the coordinates of the centroid \( G \) are:

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

The point of the centroid is \( \left( 3, \frac{14}{3} \right) \).