Question

A coordinate plane's axes range from 0 to 7, both by 1-unit increments. A triangle made up of vertices upper A, upper B, and upper C is plotted, and the coordinates of the points are given.
When the three medians of the triangle are drawn, they meet at a single point. What is the point of the centroid?

(1 point)
Responses

(3,6)
left parenthesis 3 comma 6 right parenthesis

(3,143)
left parenthesis 3 comma start Fraction 14 over 3 End Fraction right parenthesis

(3,5)
left parenthesis 3 comma 5 right parenthesis

(103,133)

Answer 1

To find the centroid of a triangle with vertices \( A(x_1, y_1) \), \( B(x_2, y_2) \), and \( C(x_3, y_3) \), we use the formula for the centroid \( G \):

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

To determine the centroid, we need the coordinates of the vertices \( A \), \( B \), and \( C \). Since you haven't provided those specific coordinates, I can’t compute the exact centroid.

However, once you have the coordinates of the points \( A \), \( B \), and \( C \), plug them into the formula above and calculate \( G \). Then compare the calculated point with the options you provided:

1. \( (3,6) \)
2. \( \left(3, \frac{14}{3}\right) \)
3. \( (3,5) \)
4. \( (103,133) \)

If you have the coordinates for the vertices, please share them, and I can help you find the centroid.