Question

Find centroid of a triangle $ABC$ with vertices $A(1,3),B(4,6)$ and $C(7,-3)$.

• A. $(4,2)$
• B. $(6,3)$
• C. $(-3,5)$
• D. $(-5,6)$

Answer 1

Answer: (A)

$(4,2)$

Let $(X_1,Y_1),(X_2,Y_2),(X_3,Y_3)$ be the vertices of triangle ABC

then co-ordinates of centroid are given by :

$x=\frac{X_1+X_2+X_3}{3}$

$y=\frac{Y_1+Y_2+Y_3}{3}$

Now as per the question

then co-ordinates of centroid are

$x=\frac{1+4+7}{3}=4$

$y=\frac{3+6-3}{3}=2$

$(4,2)$ is co-ordinates of the centroid.