Chapter 14.3, Problem 17PSC

To determine

To find the coordinates of the centroid.

Answer to Problem 17PSC

  $\left(\frac{4}{3},4\right)$

Explanation of Solution

Given:

The triangle is ABC with $A=(-2,8),B=(-6,-2)$ and $C=(12,6)$

Calculation:

The centroid of the trianglePQR can be found as follows-

  $\begin{array}{l}C(x,y)=\left(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\right)\\ C(x,y)=\left(\frac{-2-6+12}{3},\frac{8-2+6}{3}\right)\\ C(x,y)=\left(\frac{4}{3},4\right)\end{array}$

To determine

To find the coordinates of the centroid of triangle formed by joining the midpoints of the sides of triangle ABC.

Answer to Problem 17PSC

  $\left(\frac{4}{3},4\right)$

Explanation of Solution

Given:

The triangle is ABC with $A=(-2,8),B=(-6,-2)$ and $C=(12,6)$

Calculation:

The midpoint of AB, BC and CA are $(-4,3),(3,2),(5,7)$ respectively.

The centroid of the trianglecan be found as follows-

  $\begin{array}{l}C(x,y)=\left(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\right)\\ C(x,y)=\left(\frac{-4+3+5}{3},\frac{3+2+7}{3}\right)\\ C(x,y)=\left(\frac{4}{3},4\right)\end{array}$