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Mathematics

Assertion (A): The coordinates of the centroid of a triangle whose vertices are (-1, -4), (4, 3) and (6, -2) are (3, -1).

Reason (R): If the vertices of a triangle are (x1, y1), (x2, y2) and (x3, y3), then the coordinates of its centroid are (x1+x2+x33,x1+x2+x33)\Big(\dfrac{x1 + x2 + x3}{3}, \dfrac{x1 + x2 + x3}{3}\Big).

  1. A is true, R is false

  2. A is false, R is true

  3. Both A and R are true

  4. Both A and R are false

Section Formula

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Answer

By using the centroid formula,

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

The coordinates of the centroid of a triangle whose vertices are (-1, -4), (4, 3) and (6, -2) are (3, -1). Reflection, RSA Mathematics Solutions ICSE Class 10.

Substitute values we get,

⇒(x,y)=(−1+4+63,−4+3+(−2)3)⇒(x,y)=(93,−6+33)⇒(x,y)=(3,−33)⇒(x,y)=(3,−1).\Rightarrow (x,y) = \Big( \dfrac{-1 + 4 + 6}{3}, \dfrac{-4 + 3 + (-2)}{3} \Big) \\[1em] \Rightarrow (x,y) = \Big( \dfrac{9}{3}, \dfrac{-6 + 3}{3} \Big) \\[1em] \Rightarrow (x,y) = \Big( 3, \dfrac{-3}{3} \Big) \\[1em] \Rightarrow (x,y) = (3, -1).

So, Assertion (A) is true.

We know that,

If the vertices of a triangle are (x1, y1), (x2, y2) and (x3, y3), then the coordinates of its centroid are (x1+x2+x33,y1+y2+y33)\Big(\dfrac{x1 + x2 + x3}{3}, \dfrac{y1 + y2 + y3}{3}\Big).

So, Reason (R) is false.

Hence, Option 1 is the correct option.

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