If the coordinates of the vertices of a triangle be $(1, a), (2, b)$ and $(c^{2}, 3)$ , then the centroid of the triangle.

Lies at the origin

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Cannot lie on x-axis

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Cannot lie on y-axis

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None of the above

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Solution

The correct option is C Cannot lie on x-axis
Centroid is $(\frac{1 + 2 + c^{2}}{3}, \frac{a + b + 3}{3})$
Now, on
y-axis $x = 0$
$\Rightarrow \frac{3 + c^{2}}{3} = 0$
$\Rightarrow c^{2} = - 3$
Which is impossible. Hence, it cannot lie on y-axis.

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If the coordinates of the vertices of a triangle be (1,a),(2,b) and (c2,3), then the centroid of the triangle.

The correct option is C Cannot lie on x-axisCentroid is (1+2+c23,a+b+33)Now, on y-axis x=0⇒3+c23=0⇒c2=−3Which is impossible. Hence, it cannot lie on y-axis.

If the coordinates of the vertices of a triangle be $(1, a), (2, b)$ and $(c^{2}, 3)$ , then the centroid of the triangle.

The correct option is C Cannot lie on x-axis
Centroid is $(\frac{1 + 2 + c^{2}}{3}, \frac{a + b + 3}{3})$
Now, on
y-axis $x = 0$
$\Rightarrow \frac{3 + c^{2}}{3} = 0$
$\Rightarrow c^{2} = - 3$
Which is impossible. Hence, it cannot lie on y-axis.