Question

triangle abc is drawn on a coordinate plane with vertices a(-2,-3), b(4,0), and c(-2,2) and medians indicating the mid - point of each of the line segments ab, bc, and ca. prove that the medians meet at a single point by finding the centroid (1 point)
(0,0)
(0, 5/3)
(-1, 5/3)
(0, -1/3)

Explanation:

Step1: Recall centroid formula

The centroid of a triangle with vertices $(x_1,y_1)$, $(x_2,y_2)$ and $(x_3,y_3)$ has coordinates $(\frac{x_1 + x_2+x_3}{3},\frac{y_1 + y_2 + y_3}{3})$.
Here $x_1=-2$, $y_1=-3$, $x_2 = 4$, $y_2=0$, $x_3=-2$, $y_3 = 2$.

Step2: Calculate x - coordinate of centroid

$x=\frac{-2 + 4-2}{3}=\frac{0}{3}=0$.

Step3: Calculate y - coordinate of centroid

$y=\frac{-3+0 + 2}{3}=\frac{-1}{3}=-\frac{1}{3}$.

Answer:

$(0,-\frac{1}{3})$