Question

question
find the coordinates of the centroid of a triangle whose vertices are (-10, 2), (7, -11), and (12, -6). you must enter your answer as a coordinate in parenthesis.

answer attempt 1 out of 3

Explanation:

Step1: Recall the centroid formula

The centroid \(G(x, y)\) of a triangle with vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) is given by \(x=\frac{x_1 + x_2+x_3}{3}\) and \(y=\frac{y_1 + y_2 + y_3}{3}\).

Step2: Identify the coordinates of the vertices

Here, \(x_1=- 10\), \(y_1 = 2\); \(x_2=7\), \(y_2=-11\); \(x_3 = 12\), \(y_3=-6\).

Step3: Calculate the x - coordinate of the centroid

Substitute the values of \(x_1\), \(x_2\), \(x_3\) into the formula for \(x\):
\(x=\frac{-10 + 7+12}{3}=\frac{-10 + 19}{3}=\frac{9}{3}=3\)

Step4: Calculate the y - coordinate of the centroid

Substitute the values of \(y_1\), \(y_2\), \(y_3\) into the formula for \(y\):
\(y=\frac{2-11 - 6}{3}=\frac{2-17}{3}=\frac{-15}{3}=-5\)

Answer:

\((3, -5)\)