Question

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 which answer is correct and why

(3,5)
(3,5)

(3,6)
(3,6)

(103 , 133)
(103 , 133)

(13 ,13)
(13 ,13)

(3, 143
)
(3, 14 thirds)
Skip to navigation

Answer 1

The point where the three medians of a triangle meet is called the **centroid**. The centroid (often denoted as G) can be found using the coordinates of the triangle's vertices.

To determine the correct coordinates for the centroid, it is calculated as follows:

If the vertices of a triangle are \( A(x_1, y_1) \), \( B(x_2, y_2) \), and \( C(x_3, y_3) \), the centroid \( G \) can be found using the formula:

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

However, the options provided do not specify the vertices of any triangle. Without that information, we cannot definitively determine which of the given coordinates corresponds to the centroid of a specific triangle. Instead, the centroid can only be confirmed to exist at the averaged position of the triangle’s vertices.

If you have a specific triangle's coordinates or further context regarding the options listed, please provide that for a more precise answer.