Question

use the image to answer the question. when the three medians of the triangle are drawn, they meet at a single point. what is the point of the centroid? leave all results in fractions. centroid=()

Explanation:

Step1: Recall centroid formula

The centroid of a triangle with vertices $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ has coordinates $(\frac{x_1 + x_2+x_3}{3},\frac{y_1 + y_2 + y_3}{3})$. Here $(x_1,y_1)=(-3,-1),(x_2,y_2)=(2,3),(x_3,y_3)=(2,-1)$.

Step2: Calculate x - coordinate of centroid

$x=\frac{-3 + 2+2}{3}=\frac{1}{3}$

Step3: Calculate y - coordinate of centroid

$y=\frac{-1 + 3-1}{3}=\frac{1}{3}$

Answer:

$(\frac{1}{3},\frac{1}{3})$