Chapter 8.5, Problem 43SPR

To determine

To calculate:

The coordinates of the centroid of the triangle.

Answer to Problem 43SPR

The coordinates of the centroid of the triangle is $P=\left(-5,6\right)$ .

Explanation of Solution

Given information:

Coordinates of the triangle as $A\left(-1,11\right),B\left(-5,1\right),C\left(-9,6\right)$ .

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 $A\left(-1,11\right),B\left(-5,1\right),C\left(-9,6\right)$ .

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:

  $\begin{array}{l}{x}_1=-1\\ x_2=-5\\ x_3=-9\\ y_1=11\\ y_2=1\\ y_3=6\end{array}$

Thus,

  $\begin{array}{l}P=\left(\frac{-1-5-9}{3},\frac{11+1+6}{3}\right)\\ P=\left(\frac{-15}{3},\frac{18}{3}\right)\\ P=\left(-5,6\right)\end{array}$

Hence, the coordinates of the centroid of the triangle is $P=\left(-5,6\right)$ .