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Find the coordinates of centroid of a triangle whose vertices have coordinates (6,2);(- 3, 4); (3,- 9).

(- 2,1)
(1, - 2)
(2, - 1)
(- 2, - 1)

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DᴀʀᴋPᴀʀᴀᴅᴏx

[tex]\huge \bf༆ Answer ༄[/tex]

Let's solve ~

According to formula, the coordinates of Centroid of a triangle are ;

[tex] \sf x = \dfrac{x_1 + x_2 + x_3 }{3} [/tex]

[tex] \sf y = \dfrac{y_1 + y_2 + y_3 }{3} [/tex]

So, plug the coordinates of its vertices in the formula to find the required solution !

[tex]{ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:x = \dfrac{6 + ( - 3) + 3}{3} [/tex]

[tex]{ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:y = \dfrac{2+ 4 + (- 9) }{3} [/tex]

Further solving ~

[tex]{ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:x = \dfrac{6}{3} [/tex]

[tex]{ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:y = \dfrac{ - 3}{3} [/tex]

Therefore, the required coordinates are ~

[tex]{ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:x = 2[/tex]

[tex]{ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:y = - 1[/tex]

Correct choice is ;

[tex]\overbrace{  \underbrace{\underline{ \boxed{ \sf (2 ,-1)}}}}[/tex]

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