Question

what ia the centeroid of the traingle ABC,where co-ordinate of A,B,C are (6,4) ,(3,-1) ,(0,0)​

Answer 1

Given :-

The points A ( 6 , 4 ), B ( 3 , -1 ) and C ( 0 , 0 ) are the vertices of the triangle ABC.

To Find :-

Coordinates of the centroid of triangle ABC.

Solution :-

Let the coordinates of the centroid be ( x , y ).

$\underline{\boxed{\bf Centroid \ formula = \left( \dfrac{x_1+x_2+x_3}{3} \ , \ \dfrac{y_1+y_2+y_3}{3} \right)}}$

Here :-

$\bullet \sf \ x_1=4 \\\\\bullet \sf \ x_2=3 \\\\\bullet \sf \ x_3 = 0 \\\\\bullet \sf \ y_1 = 4 \\\\\bullet \sf \ y_2 = -1 \\\\\bullet \sf \ y_3 = 0$

x coordinate :-

$\longrightarrow \sf \dfrac{x_1+x_2+x_3}{3} \\\\\longrightarrow \dfrac{6+3+0}{3} \\\\\longrightarrow \dfrac{9}{3} \\\\\longrightarrow \bf 3$

y coordinate :-

$\longrightarrow \sf \dfrac{y_1+y_2+y_3}{3} \\\\\longrightarrow \dfrac{4-1+0} {3} \\\\\longrightarrow \dfrac{3}{3} \\\\\longrightarrow \bf 1$

Coordinates of centroid = ( 3 , 1 )

Answer 2

Step-by-step explanation:

The points A ( 6 , 4 ), B ( 3 , -1 ) and C ( 0 , 0 ) are the vertices of the triangle ABC.

To Find :-

Coordinates of the centroid of triangle ABC.

Solution :-

Let the coordinates of the centroid be ( x , y ).

$\underline{\boxed{\bf Centroid \ formula = \left( \dfrac{x_1+x_2+x_3}{3} \ , \ \dfrac{y_1+y_2+y_3}{3} \right)}}[tex]</p><p></p><h3>Here :-</h3><p></p><p>[tex]\begin{gathered}\bullet \sf \ x_1=4 \\\\\bullet \sf \ x_2=3 \\\\\bullet \sf \ x_3 = 0 \\\\\bullet \sf \ y_1 = 4 \\\\\bullet \sf \ y_2 = -1 \\\\\bullet \sf \ y_3 = 0\end{gathered}$

$\begin{gathered}\longrightarrow \sf \dfrac{x_1+x_2+x_3}{3} \\\\\longrightarrow \dfrac{6+3+0}{3} \\\\\longrightarrow \dfrac{9}{3} \\\\\longrightarrow \bf 3\end{gathered} </p><p>⟶$

$\begin{gathered}\longrightarrow \sf \dfrac{y_1+y_2+y_3}{3} \\\\\longrightarrow \dfrac{4-1+0} {3} \\\\\longrightarrow \dfrac{3}{3} \\\\\longrightarrow \bf 1\end{gathered}$

Coordinates of centroid = ( 3 , 1 )