Question

The centroid if the $∆ABC$, where $A=\left(2,3\right),B=\left(8,10\right)$ and $C=\left(5,5\right)$ is

• A. $\left(5,6\right)$
• B. $\left(6,5\right)$
• C. $\left(6,6\right)$
• D. $\left(15,18\right)$

Answer 1

The correct option is A

$\left(5,6\right)$

Explanation for the correct option:

Finding the centroid:

Centroid of the triangle formed by vertices $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ is given by

$x=\frac{x_1+x_2+x_3}{3}$ and $y=\frac{y_1+y_2+y_3}{3}$

Substitute the values.

$$\begin{gathered} \therefore x=\frac{2+8+5}{3} \\ =5 \end{gathered}$$

and $$\begin{gathered} y=\frac{3+10+5}{3} \\ =6 \end{gathered}$$

Therefore, option (A) is correct.