Question

if △abc has vertices a(0, 0), b(4, 2) and c(0, 10), what are the coordinates of the centroid of △abc?

a) (0, 5)
b) (1, 3)
c) (4/3, 4)
d) (4, 3)

Explanation:

Step1: Recall centroid formula

The centroid of a triangle with vertices $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ is given by $(\frac{x_1 + x_2+x_3}{3},\frac{y_1 + y_2 + y_3}{3})$.

Step2: Identify vertex - coordinates

Here $x_1 = 0,y_1 = 0,x_2=4,y_2 = 2,x_3 = 0,y_3 = 10$.

Step3: Calculate x - coordinate of centroid

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

Step4: Calculate y - coordinate of centroid

$y=\frac{0 + 2+10}{3}=\frac{12}{3}=4$.

Answer:

C. $(\frac{4}{3},4)$