Answer:
The center of the given triangle FGH is
[tex](\frac{8}{3},-\frac{4}{3})[/tex]
Step-by-step explanation:
Given that the triangle FGH has vertices (0,4),(0,-4) and (8,-4) respectively.
To find the center of the given triangle FGH:
The centroid of a triangle is its center-most point.
Therefore we can simply find the centroid
Let O be the centroid of the triangle FGH
We have Centroid formula [tex]Ox=\frac{Fx+Gx+Hx}{3}[/tex]
and [tex]Oy=\frac{Fy+Gy+Hy}{3}[/tex]
[tex]Ox=\frac{Fx+Gx+Hx}{3}[/tex]
[tex]Ox=\frac{0+0+8}{3}[/tex]
[tex]Ox=\frac{8}{3}[/tex]
and [tex]Oy=\frac{Fy+Gy+Hy}{3}[/tex]
[tex]Oy=\frac{4-4-4}{3}[/tex]
[tex]Oy=\frac{0-4}{3}[/tex]
[tex]Oy=\frac{-4}{3}[/tex]
Therefore [tex]Oy=-\frac{4}{3}[/tex]
The centroid of the triangle FGH is
[tex](\frac{8}{3},-\frac{4}{3})[/tex]
That is the center of the given triangle FGH is
[tex](\frac{8}{3},-\frac{4}{3})[/tex]
