Question

If A( 2 ,5) ,B(4 , 9) ,C (3 ,1 ) are vertices of triangle then coordinates of centroid are.
( 5 , 3)
( 3 , 5)
( 3 , 1)
( 5 , 1)​

Answer 1

ㅤ★Answer :-

Centroid of the triangle is(3,5) [B]

ㅤ★Given :-

Vertices of triangle A=(2,5) , B=(9,4) , C= (3,1)

ㅤㅤㅤ★ To find :-

Centroid of the triangle

‎‎ㅤㅤ★Diagram :-

$\setlength{\unitlength}{2.5mm}\begin{picture}(0,0)\linethickness{0.3mm}\qbezier(0,0)(0,0)(8,17)\qbezier(0,0)(0,0)(18,0)\qbezier(18,0)(18,0)(8,17)\put(8,17.8){\sf A=(2,5)}\put( - 1, - 1){\sf B=(4,9)}\put(18,-1){\sf C=(3 1)}\put(8, - 1.5){\sf }\put(15,8.1){\sf }\put( - 0,8.1){\sf }\end{picture}$

ㅤㅤ★ EXPLANATION :-

As, we know that,

$\bigstar \boxed{ \underline{ \pink{ \bf{C entroid(G) = \bigg(\frac{x_1 + x_2 + x_3}{3} \: , \frac{y_1 + y_2 + y_3}{3} \bigg) }}}}$

So,

ㅤㅤA= (2,5)=(x₁ ,y₁)

ㅤㅤB = (4,9) = (x₂,y₂)

ㅤㅤC = (3, 1) = (x₃, y₃)

Substituting the values,

$\: \: \: \: \: \: \: \: \: \dashrightarrow\bf \: \bigg( \dfrac{2 + 4 + 3}{3} , \dfrac{5 + 9+ 1}{3} \bigg)$

$\: \: \: \: \: \: \: \: \: \dashrightarrow\bf \: \bigg( \dfrac{9}{3} , \dfrac{15}{3} \bigg)$

$\: \: \: \: \: \: \: \: \: \dashrightarrow\bf \: \bigg( 3 ,5\bigg)$

So, the Centroid of the triangle is (3,5)

Note :- Kindly see the answer from web to sèe the diagram clearly.