Given:
Vertices of a triangle are D(0,5), E(2,0) and F(-4,2).
To find:
The intersection point of medians DG and EH.
Solution:
We know that, intersection point of all the medians of a triangle is called centroid.
The formula of centroid is
![Centroid=\left(\dfrac{x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3}\right)](https://tex.z-dn.net/?f=Centroid%3D%5Cleft%28%5Cdfrac%7Bx_1%2Bx_2%2Bx_3%7D%7B3%7D%2C%5Cdfrac%7By_1%2By_2%2By_3%7D%7B3%7D%5Cright%29)
Vertices of a triangle are D(0,5), E(2,0) and F(-4,2). So, the centroid of the triangle is
![Centroid=\left(\dfrac{0+2+(-4)}{3},\dfrac{5+0+2}{3}\right)](https://tex.z-dn.net/?f=Centroid%3D%5Cleft%28%5Cdfrac%7B0%2B2%2B%28-4%29%7D%7B3%7D%2C%5Cdfrac%7B5%2B0%2B2%7D%7B3%7D%5Cright%29)
![Centroid=\left(\dfrac{-2}{3},\dfrac{7}{3}\right)](https://tex.z-dn.net/?f=Centroid%3D%5Cleft%28%5Cdfrac%7B-2%7D%7B3%7D%2C%5Cdfrac%7B7%7D%7B3%7D%5Cright%29)
![Centroid=\left(-0.666...,2.333\right)](https://tex.z-dn.net/?f=Centroid%3D%5Cleft%28-0.666...%2C2.333%5Cright%29)
Round each coordinate to the nearest tenth.
![Centroid=\left(-0.7,2.3\right)](https://tex.z-dn.net/?f=Centroid%3D%5Cleft%28-0.7%2C2.3%5Cright%29)
Therefore, the correct option is C.