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 $(x_3,y_3)$ has coordinates $(\frac{x_1 + x_2+x_3}{3},\frac{y_1 + y_2 + y_3}{3})$. Here, $A(5,5)$ where $x_1 = 5,y_1=5$, $B(1,7)$ where $x_2 = 1,y_2 = 7$ and $C(3,2)$ where $x_3=3,y_3 = 2$.

Step2: Calculate x - coordinate of centroid

$x=\frac{5 + 1+3}{3}=\frac{9}{3}=3$.

Step3: Calculate y - coordinate of centroid

$y=\frac{5 + 7+2}{3}=\frac{14}{3}$.

Answer:

$(3,\frac{14}{3})$