If centroid of the triangle formed by the points -2- 2 -3 - 1- and 1-3 is 13- 13- then centroid of the triangle formed by the points 2 -1- -31-3 - 2 -2-3 and 0-3 - is

Centriod of the triangle formed by the given points is (α^2+3 α+13,4+α3)≡(13, 13) ⇒α= 3 ∴ Centroid of the triangle formed by (2 α 1, α^3), (1 3 α, 2 α^2+3) and ...

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Standard IX

Mathematics

Incircle and Its Construction

If centroid o...

Question

If centroid of the triangle formed by the points $(α^{2}, 2 α) (3 α, 1 - α)$ and $(1, 3)$ is $(\frac{1}{3}, \frac{1}{3})$ , then centroid of the triangle formed by the points $(2 α - 1, α^{3}) (1 - 3 α, 2 α^{2} + 3)$ and $(0, - 3 α)$ is

(1, 1)

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(1, 0)

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(\frac{1}{3}, 1)

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(0, 1)

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Solution

The correct option is A $(1, 1)$
Centriod of the triangle formed by the given points is
$(\frac{α^{2} + 3 α + 1}{3}, \frac{4 + α}{3}) \equiv (\frac{1}{3}, \frac{1}{3})$
$\Rightarrow α = - 3$

$∴$ Centroid of the triangle formed by $(2 α - 1, α^{3}), (1 - 3 α, 2 α^{2} + 3)$ and $(0, - 3 α)$ is
$(\frac{- α}{3}, \frac{α^{3} + 2 α^{2} - 3 α + 3}{3}) \equiv (1, 1)$

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If centroid of the triangle formed by the points (α2,2α)(3α,1−α) and (1,3) is (13,13), then centroid of the triangle formed by the points (2α−1,α3)(1−3α,2α2+3) and (0,−3α) is

The correct option is A (1,1)Centriod of the triangle formed by the given points is (α2+3α+13,4+α3)≡(13,13) ⇒α=−3 ∴ Centroid of the triangle formed by (2α−1,α3),(1−3α,2α2+3) and (0,−3α) is (−α3,α3+2α2−3α+33)≡(1,1)

If centroid of the triangle formed by the points $(α^{2}, 2 α) (3 α, 1 - α)$ and $(1, 3)$ is $(\frac{1}{3}, \frac{1}{3})$ , then centroid of the triangle formed by the points $(2 α - 1, α^{3}) (1 - 3 α, 2 α^{2} + 3)$ and $(0, - 3 α)$ is