Question

Two vertices of Triangle ABC are A(-3,0), B(5,-2) and C(-8,5), Then the centroid of Triangle ABC is ____________??????

Answer 1

Answer:

-8 is the correct answer in this question

Answer 2

♣ Qᴜᴇꜱᴛɪᴏɴ :

• Two vertices of △ABC are A(-3,0), B(5,-2) and C(-8,5), Then the centroid of △ABC is  

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\put(0, 1.6){ \bf }\cm }\qbezier(5,0)(5,0)(3,3)\put(5.0, 1.6){ \bf }\qbezier(5,0)(1,0)(1,0)\put(2.4, - 0.9){ \bf }\put(2.85,3.2){ \bf A(-3\:,0) }\put(0.5,-0.4){ \bf C(-8\:,5) }\put(5.2,-0.3){ \bf B(5\:,-2) }\end{picture}$

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♣ ᴀɴꜱᴡᴇʀ :

${\sf{G \:=\:\left(-2\:,1\right)}$

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♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ :

△ABC have vertices :

• A (-3 , 0)
• B (5 , -2)
• C (-8 , 5)

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\put(0, 1.6){ \bf }\cm }\qbezier(5,0)(5,0)(3,3)\put(5.0, 1.6){ \bf }\qbezier(5,0)(1,0)(1,0)\put(2.4, - 0.9){ \bf }\put(2.85,3.2){ \bf A(-3\:,0) }\put(0.5,-0.4){ \bf C(-8\:,5) }\put(5.2,-0.3){ \bf B(5\:,-2) }\end{picture}$

A (-3 , 0)     B (5 , -2)     C (-8 , 5)

    x₁   y₁          x₂   y₂          x₃   y₃

The Centroid Formula is Given by :

$\large\boxed{\sf{G \:=\:\left(\dfrac{x_1+x_2+x_3}{3}\:,\dfrac{y_1+y_2+y_3}{3}\right)}}$

From The Centroid Formula :

${\sf{G \:=\:\left(\dfrac{-3+5+(-8)}{3}\:,\dfrac{0+(-2)+5}{3}\right)}$

${\sf{G \:=\:\left(\dfrac{2+(-8)}{3}\:,\dfrac{-2)+5}{3}\right)}$

${\sf{G \:=\:\left(\dfrac{-6}{3}\:,\dfrac{3}{3}\right)}$

${\sf{G \:=\:\left(-2\:,1\right)}$

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