Question

Find the coordinates of the centroid of a $\Delta ABC$ whose vertices are

A(5,10), B (10,0), C(5,4)

• A. $(\frac{20}{3},8)$
• B. $(\frac{20}{3},-8)$
• C. (4,-5)
• D. (6,9)

Answer 1

The correct option is A

$(\frac{20}{3},8)$

Vertices of a $△ABC$ are $A(x_1,y_1),B(x_2,y_2)$ and $C(x_3,y_3)$

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

$A(5,10)\Rightarrow x_1=5,y_1=10$

$B(10,10)\Rightarrow x_2=10,y_2=10$

$C(5,4)\Rightarrow x_3=5,y_3=4$

Centroid $=(\frac{5+5+10}{3},\frac{24}{3})$

centroid $=(\frac{20}{3},8)$