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Mathematics

Two vertices of a ΔABC are A(-1, 4) and B(5, 2) and its centroid is (0, -3). The coordinates of C are :

  1. (4, 3)

  2. (4, 15)

  3. (-4, -15)

  4. (-15, -4)

Section Formula

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Answer

Let the coordinates of C be (x, y).

Two vertices of a ΔABC are A(-1, 4) and B(5, 2) and its centroid is (0, -3). The coordinates of C are : Reflection, RSA Mathematics Solutions ICSE Class 10.

By centroid formula,

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

Given,

G(0, -3) is the centroid of the triangle.

Substituting values we get :

⇒(0,−3)=(−1+5+x3,4+2+y3)⇒(0,−3)=(4+x3,6+y3)⇒0=4+x3 and −3=6+y3⇒4+x=0 and 6+y=−9⇒x=−4 and y=−9−6⇒x=−4 and y=−15.\Rightarrow (0, -3) = \Big(\dfrac{-1 + 5 + x}{3}, \dfrac{4 + 2 + y}{3}\Big) \\[1em] \Rightarrow (0, -3) = \Big(\dfrac{4 + x}{3}, \dfrac{6 + y}{3}\Big) \\[1em] \Rightarrow 0 = \dfrac{4 + x}{3} \text{ and } -3 = \dfrac{6 + y}{3} \\[1em] \Rightarrow 4 + x = 0 \text{ and } 6 + y = -9 \\[1em] \Rightarrow x = -4 \text{ and } y = -9 - 6 \\[1em] \Rightarrow x = -4 \text{ and } y = -15.

C = (x, y) = (-4, -15).

Hence, Option 3 is the correct option.

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