Hi everybody
Show that the centroid of a triangle coincides with that of the triangle formed by the mid points of the sides.
Thank you all
Sridhar
For a triangle, the centriod is just the "average" of the vertices. That is, if the vertices are $\displaystyle (x_1, y_1)$, $\displaystyle (x_2, y_2)$, and $\displaystyle (x_3, y_3)$, in some coordinate system, then the centroid is at $\displaystyle \left(\frac{x_1+ x_2+ x_3}{3}, \frac{y_1+ y_2+ y_3}{3}\right)$.
Of course, the midpoints of the sides are $\displaystyle \left(\frac{x_1+ x_2}{2}, \frac{y_1+ y_2}{2}\right)$, $\displaystyle \left(\frac{x_2+ x_3}{2}, \frac{y_2+ y_3}{2}\right)$, and $\displaystyle \left(\frac{x_1+ x_3}{2}, \frac{y_1+ y_3}{2}\right)$. Use the formula above to find the centroid of that triangle.