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A(1, 4), B(4, 1) and C(x, 4) are the vertices of ΔABC. If the centroid of the triangle is G(4, 3), then x is equal to:

  1. 2

  2. 1

  3. 7

  4. 4

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Answer

Given,

The vertices of the triangle be A(1, 4), B(4, 1) and C(x, 4). The centroid G of a triangle is given by the formula:

A(1, 4), B(4, 1) and C(x, 4) are the vertices of ΔABC. If the centroid of the triangle is G(4, 3), then x is equal to: Reflection, RSA Mathematics Solutions ICSE Class 10.

Centroid = (x1+x2+x33,y1+y2+y33)\Big(\dfrac{x1 + x2 + x3}{3}, \dfrac{y1 + y2 + y3}{3}\Big)

Substituting the given values we get :

⇒(4,3)=(1+4+x3,4+1+43)⇒(4,3)=(5+x3,93)⇒(4,3)=(5+x3,3)⇒4=5+x3⇒12=5+x⇒x=12−5=7.\Rightarrow (4, 3) = \Big(\dfrac{1 + 4 + x}{3}, \dfrac{4 + 1 + 4}{3}\Big) \\[1em] \Rightarrow (4, 3) = \Big(\dfrac{5 + x}{3}, \dfrac{9}{3}\Big) \\[1em] \Rightarrow (4, 3) = \Big(\dfrac{5 + x}{3}, 3\Big) \\[1em] \Rightarrow 4 = \dfrac{5 + x}{3} \\[1em] \Rightarrow 12 = 5 + x \\[1em] \Rightarrow x = 12 - 5 = 7.

Hence, Option 3 is the correct option.

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