Question

find the centroid of the triangle whose vertices are L(3,-7) M(4,3) N(11,-4)​

Answer 1

Answer:

Centroid = (6, -8/3)

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Step-by-step explanation:

A centroid of a triangle refers to the point where all 3 medians of the triangle intersect at.

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The centroid (generally denoted by G) of a triangle with three points A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) is given by;

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$\sf \dashrightarrow G(x, y) = \Bigg\{\dfrac{x_1 + x_2 + x_3}{3} , \dfrac{y_1 + y_2 + y_3}{3} \Bigg\}$

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We have three points L(3,-7) M(4,3) and N(11,-4)​.

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Therefore we have;

• x₁ = 3

• x₂ = 4

• x₃ = 11

• y₁ = -7

• y₂ = 3

• y₃ = -4

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We know that;

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$\sf \dashrightarrow G(x, y) = \Bigg\{\dfrac{x_1 + x_2 + x_3}{3} , \dfrac{y_1 + y_2 + y_3}{3} \Bigg\}$

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On substituting the values of the coordinates in the equation we get;

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$\sf \dashrightarrow G(x, y) = \Bigg\{\dfrac{3 + 4 + 11}{3} , \dfrac{-7 + 3 + (-4)}{3} \Bigg\}$

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$\sf \dashrightarrow G(x, y) = \Bigg\{\dfrac{18}{3} , \dfrac{-4 - 4}{3} \Bigg\}$

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$\sf \dashrightarrow G(x, y) = \Bigg\{6 , \dfrac{-8}{3} \Bigg\}$

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[Diagram attached for reference]

Answer 2

Answer:

$⇢G(x,y)={6,3−8}$