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? (1 point)

Explanation:

Step1: Recall centroid formula

The centroid of a triangle with vertices $(x_1,y_1)$, $(x_2,y_2)$ and $(x_3,y_3)$ is given by $(\frac{x_1 + x_2+x_3}{3},\frac{y_1 + y_2 + y_3}{3})$. Here $A(-5,1)$, $B(1,7)$ and $C(1, - 5)$, so $x_1=-5$, $y_1 = 1$, $x_2=1$, $y_2=7$, $x_3=1$, $y_3=-5$.

Step2: Calculate x - coordinate of centroid

$x=\frac{-5 + 1+1}{3}=\frac{-3}{3}=-1$.

Step3: Calculate y - coordinate of centroid

$y=\frac{1 + 7-5}{3}=\frac{3}{3}=1$.

Answer:

$(-1,1)$