Question

use the image to answer the question. prove that when the three medians of the triangle are drawn, they meet at a single point. what is the point of the centroid? (1 point) (8/3,2) (3,2) (10/3,0) (3/8,2)

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 $A(4,-2)$, $B(6,5)$ and $C(-1,3)$, so $x_1 = 4$, $y_1=-2$, $x_2 = 6$, $y_2 = 5$, $x_3=-1$, $y_3 = 3$.

Step2: Calculate x - coordinate of centroid

$x=\frac{4 + 6+( - 1)}{3}=\frac{4+6 - 1}{3}=\frac{9}{3}=3$.

Step3: Calculate y - coordinate of centroid

$y=\frac{-2 + 5+3}{3}=\frac{-2 + 8}{3}=\frac{6}{3}=2$.

Answer:

$(3,2)$