Chapter 8.5, Problem 42SPR

To determine

To calculate:

The coordinates of the centroid of the triangle.

Answer to Problem 42SPR

The coordinates of the centroid of the triangle is $P=\left(-3,-7\right)$ .

Explanation of Solution

Given information:

Coordinates of the triangle as $X\left(-3,-2\right),Y\left(1,-12\right),Z\left(-7,-7\right)$ .

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 $\Delta XYZ$ with $X\left(-3,-2\right),Y\left(1,-12\right),Z\left(-7,-7\right)$ .

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:

  $\begin{array}{l}{x}_1=-3\\ x_2=1\\ x_3=-7\\ y_1=-2\\ y_2=-12\\ y_3=-7\end{array}$

Thus,

  $\begin{array}{l}P=\left(\frac{-3+1-7}{3},\frac{-2-12-7}{3}\right)\\ P=\left(\frac{-9}{3},\frac{-21}{3}\right)\\ P=\left(-3,-7\right)\end{array}$

Hence, the coordinates of the centroid of the triangle is $P=\left(-3,-7\right)$ .