Question

unit 6 formal proofs > lesson 9 medians of a triangle the three medians of △abc meet at a single point. what is the point of the centroid? express all results in fractions (1 point)

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 $(\frac{x_1 + x_2+x_3}{3},\frac{y_1 + y_2 + y_3}{3})$.

Step2: Identify vertex coordinates

Here, $A(2,2)$, $B(8,2)$ and $C(4,7)$. So $x_1 = 2$, $y_1=2$, $x_2 = 8$, $y_2 = 2$, $x_3=4$, $y_3 = 7$.

Step3: Calculate x - coordinate of centroid

$x=\frac{2 + 8+4}{3}=\frac{14}{3}$.

Step4: Calculate y - coordinate of centroid

$y=\frac{2 + 2+7}{3}=\frac{11}{3}$.

Answer:

$(\frac{14}{3},\frac{11}{3})$