Answer:
[tex](x,y)=(0,\frac{-2}{3})[/tex]
Step-by-step explanation:
Given : Vertices of Triangle [tex]P(x_1,y_1)=(-4,-1)[/tex] , [tex]Q(x_2,y_2)=(2, 2)[/tex] and [tex]R(x_3,y_3)=(2,-3)[/tex]
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:
[tex](x,y)=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})[/tex]
Where, [tex]x_1,x_2,x_3,y_1,y_2,y_3[/tex] are the coordinates of the centroid
Substituting the values in the formula gives us:
[tex](x,y)=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})[/tex]
[tex](x,y)=(\frac{-4+2+2}{3},\frac{-1+2-3}{3})[/tex]
[tex](x,y)=(\frac{0}{3},\frac{-2}{3})[/tex]
Therefore, [tex](x,y)=(0,\frac{-2}{3})[/tex]
