Question

Find the centroid of the triangle whose vertices are (-7,6).(6.-7).(-7,-6).​

Answer 1

A n s w e r

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G i v e n

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• Vertices of triangle are (-7,6) , (6,-7) , (-7,-6)

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F i n d

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• Centroid of the triangle

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S o l u t i o n

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Centroid of a given triangle is located at the intersecting point of all three medians of the triangle

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It can be easily localized by the vertices of triangle

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For a triangle with vertices (x1, y1) , (x2, y2) , (x3, y3) the centroid will be -

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➠ $\sf \boxed { \dfrac { (x1 + x2 + x3) } { 3 } , \dfrac { (y1 + y2 + y3) } { 3 } }$

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For the given triangle -

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• x1 = -7

• x2 = 6

• x3 = -7

• y1 = 6

• y2 = -7

• y3 = -6

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⟮ Putting the above values ⟯

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: ➜ $\sf \bigg\lgroup \dfrac { (x1 + x2 + x3) } { 3 } , \dfrac { (y1 + y2 + y3) } { 3 } \bigg\rgroup$

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: ➜ $\sf \bigg\lgroup \dfrac { (-7 + 6 - 7) } { 3 } , \dfrac { (6 - 7 - 6) } { 3 } \bigg\rgroup$

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: ➜ $\sf \bigg\lgroup \dfrac { (-8) } { 3 } , \dfrac { (-7) } { 3 } \bigg\rgroup$

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• Hence the coordinates of centroid are $\sf \bigg\lgroup \dfrac { (-8) } { 3 } , \dfrac { (-7) } { 3 } \bigg\rgroup$

Answer 2

Given :

• $(x_1,y_1)=(-7,6)$
• $(x_2,y_2)=(6,-7)$
• $(x_3,y_3) = (-7,-6)$

To Find :

• Centroid of the Triangle $G(x,y)$

Solution :

• Co-ordinates of the centroid of the triangle is the average of the coordinates of the vertices.

$\displaystyle{G(x,y) = \[\left ( \frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3} \right)\]}$

$\implies \displaystyle{\[\left(\frac{-7+6-7}{3},\frac{6-7-6}{3 }\right)\]}$

$\implies \displaystyle{\[\left(\frac{-14+6}{3}, \frac{-7}{3}\right )\]}$

$\implies \displaystyle{\[ \left( \frac{-8}{3}, \frac{-7}{3}\right)\]}$

Required answer :

Centroid of the given triangle is ${\displaystyle{\[ \left(\frac{-8}{3}, \frac{-7}{3} \right)\]}}$