Answer:
The centroid is located at (3,3)
Step-by-step explanation:
Centroid Of A Triangle
The centroid of a triangle is the point where its three medians intersect. It is also the center of gravity of the triangle. The medians are lines that go from each vertex to the midpoint of the opposite side.
Given A(ax,by), B(bx,by), C(cx,cy) the points of the vertices, then the coordinates of the centroid [tex]P(x_c,y_c)[/tex] are
[tex]\displaystyle x_c=\frac{ax+bx+cx}{3}[/tex]
[tex]\displaystyle y_c=\frac{ay+by+cy}{3}[/tex]
The vertices are (0,1) (2,6) (7,2), thus
[tex]\displaystyle x_c=\frac{0+2+7}{3}=3[/tex]
[tex]\displaystyle y_c=\frac{1+6+2}{3}=3[/tex]
The centroid is located at (3,3)
