Question

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 1

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 (x₁,y₁), (x₂, y₂) and (x₃, y₃)is given below:

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

⇒ sinθ – cosθ = 2cosθ + 2sinθ 

⇒ tanθ = -3 

∴ tanθ = − 3 

Hence, tanθ = − 3