Question

the centroid of a triangle formed by the points( 0,0) (cos teta ,sin teta ) and( sin teta ,_cos teta,) lies on the line y =2×, then teta=​

Answer 1

Answer:

The answer is tan⁻¹(-1/3)

Step-by-step explanation:

If the vertices of a triangle are given by ( x₁ , y₁ ) , ( x₂ , y₂ ) , ( x₃ , y₃ ) then

the centroid of the triangle will be , ( x₁ + x₂ + x₃/3 , y₁ + y₂ + y₃/3 )

In this case , the given three vertices of the triangle are ,

( 0,0) (cosθ ,sinθ ) and( sinθ ,-cosθ)

then , the centroid of the triangle is ,

( sinθ + cosθ/3 , sinθ - cosθ/3 )

this point lies on the line y = 2x.

then , sinθ + cosθ/3 = 2/3( sinθ - cosθ )

⇒ -sinθ = 3cosθ

⇒ tanθ = (- 1)/3

⇒ θ = tan⁻¹(-1/3)