Question

Using the fact that a centroid of a triangle lies at the intersection of the triangles medians, which is the point that lies one third of the way from each side toward the opposite vertex. Find the centroid of the triangle whose vertices are (0,0), (a,0), and (0,a). Assume a>0 and b>0.

Answer 1

x =
`(a)/(3)`

y =
`(b)/(3)`

Explanation:

Recall that he center point of a triangle is given by the formula
`(\frac{x_(1)+x_(2)+x_(3)}3,\frac{y_(1)+y_(2)+y_(3)}3)`, where
`(x_(1),y_(1)),( x_(2),y_(2)),(x_(3),y_(3))` indicate the vertices of the tringle.

Therefore:

`(\frac{0+a+0}3,\frac{0+0+b}3)` =
`((a)/(3),(b)/(3))`