Question

What are the coordinates of the centroid of a triangle with vertices P(−4, −1) , Q(2, 2) , and R(2, −3) ?

Answer 1

The centroid is: x=0, y = -2/3

Answer 2

Answer:

$(x,y)=(0,\frac{-2}{3})$

Step-by-step explanation:

Given : Vertices of Triangle $P(x_1,y_1)=(-4,-1)$ , $Q(x_2,y_2)=(2, 2)$ and $R(x_3,y_3)=(2,-3)$

To find : Centroid of a triangle

The centroid of a triangle is the point of intersection of the three medians of the triangle.

The formula to calculate the centroid of a triangle is:

$(x,y)=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

Where, $x_1,x_2,x_3,y_1,y_2,y_3$  are the coordinates of the centroid

Substituting the values in the formula gives us:

$(x,y)=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

$(x,y)=(\frac{-4+2+2}{3},\frac{-1+2-3}{3})$

$(x,y)=(\frac{0}{3},\frac{-2}{3})$

Therefore, $(x,y)=(0,\frac{-2}{3})$