Chapter 8.5, Problem 41SPR

To determine

To calculate:

The coordinates of the centroid of the triangle.

Answer to Problem 41SPR

The coordinates of the centroid of the triangle is $P=\left(7,4\right)$ .

Explanation of Solution

Given information:

Coordinates of the triangle as $A\left(2,2\right),B\left(7,8\right),C\left(12,2\right)$ .

Formula used:

The centroid of three points formula:

  $P=\left(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\right)$

Calculation:

To find the coordinates of the centroid of the $\Delta ABC$ with $A\left(2,2\right),B\left(7,8\right),C\left(12,2\right)$ .

Using the centroid of three points formula:

  $P=\left(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\right)$

Substitute the values in above equation as:

  $\begin{array}{l}{x}_1=2\\ x_2=7\\ x_3=12\\ y_1=2\\ y_2=8\\ y_3=2\end{array}$

Thus,

  $\begin{array}{l}P=\left(\frac{2+7+12}{3},\frac{2+8+2}{3}\right)\\ P=\left(\frac{21}{3},\frac{12}{3}\right)\\ P=\left(7,4\right)\end{array}$

Hence, the coordinates of the centroid of the triangle is $P=\left(7,4\right)$ .