Question

question
find the coordinates of the centroid of a triangle whose vertices are (12, 5), (8, 7), and (10, 12). you must enter your answer as a coordinate in parenthesis.
answer attempt 1 out of 3
additional solution no solution

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 the formula:

$$ x=\frac{x_1 + x_2 + x_3}{3}, \quad y=\frac{y_1 + y_2 + y_3}{3} $$

Step2: Identify the coordinates

Given vertices \((12, 5)\), \((8, 7)\), and \((10, 12)\), we have \(x_1 = 12\), \(y_1 = 5\), \(x_2 = 8\), \(y_2 = 7\), \(x_3 = 10\), \(y_3 = 12\).

Step3: Calculate the x - coordinate of the centroid

Substitute the \(x\) - values into the formula for \(x\):

$$ x=\frac{12 + 8+10}{3}=\frac{30}{3}=10 $$

Step4: Calculate the y - coordinate of the centroid

Substitute the \(y\) - values into the formula for \(y\):

$$ y=\frac{5 + 7+12}{3}=\frac{24}{3}=8 $$

Answer:

\((10, 8)\)