Question

use the text to answer the question.
B(1,7) A(5,5) C(3,2)
when the medians of the triangle are drawn, they meet at a single point. what is the point of the centroid?
a. (10/3,13/3)
b. (3,14/3)
c.(3,5)
d.(3,6)

Answer 1

To find the centroid of a triangle with vertices at \( A(5, 5) \), \( B(1, 7) \), and \( C(3, 2) \), we use the formula for the centroid, which is given by:

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

Substituting in the coordinates of the vertices:

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

Now, plug these values into the centroid formula:

\[
G = \left( \frac{5 + 1 + 3}{3}, \frac{5 + 7 + 2}{3} \right)
\]

Calculating the x-coordinate:

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

Calculating the y-coordinate:

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

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

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

Comparing with the options provided, the correct answer is:

**b. (3, 14/3)**