Question

Find the centroid of a triangle, whose vertices are $\left(3,-5\right),\left(-7,4\right)$ and $\left(10,2\right)$.

Answer 1

Step 1: Accumulate all the given information in systematic order.

Let $A,B$ and $C$ be the vertices of the triangle whose coordinates are $\left(3,-5\right),\left(-7,4\right)$ and $\left(10,2\right)$ respectively.

Now, we know that the coordinates of the centroid of a triangle are;

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

Step 2: Finding the centroid of the triangle:

Here

$x_1=3,y_1=-5,x_2=-7,y_2=4,x_3=10and{y}_3=-2$

By putting the values in the above formula, we get;

Centroid of the triangle

$=\left(\frac{3+(-7)+10}{3},\frac{-5+4+(-2)}{3}\right)$

$=\left(\frac{6}{3},\frac{-3}{3}\right)=\left(2,-1\right)$

Hence, the coordinates of centroid are $2,-1$