Q. 35.0( 2 Votes )

# If the centroid of a triangle formed by the points (0, 0), (cos θ, sin θ) and (sinθ, - cosθ) lies on the line y = 2x, then write the value of tanθ.

Answer :

__Given:__

The points (0, 0), (cos θ, sin θ) and (sinθ, - cosθ) lies on the line y = 2x

__To find:__

The value of tanθ.

**Explanation:**

The centroid of a triangle with vertices (x_{1},y_{1}), (x_{2}, y_{2}) and (x_{3}, y_{3})is given below:

Therefore, the centre of the triangle having vertices (0, 0,), (cos θ, sin θ) and (sin θ, − cos θ) is

This point lies on the line y = 2x.

⇒ sinθ – cosθ = 2cosθ + 2sinθ

⇒ tanθ = -3

∴ tanθ = − 3

Hence, tanθ = − 3

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