In math worksheet on distance between the polar co-ordinates, we will solve different types of questions.
Recall the formula for the length of the line-segment joining the points:
(r₁, θ ₁) and (r₂, θ₂) is √[r₁² + r₂ ² - 2r₁ r₂ cos(θ₂ - θ₁)].
Review more about the distance between the two points in the polar co-ordinates and the different types of examples Click Here.
Using the above formula to solve the below questions given in the worksheet on distance between the polar co-ordinates.
1. Find the length of the line-segment joining the points :
(i) (8, π/3) and (3, π/6)
(ii) (-a√3, -30°) and (–a, 60°).
2. Show that the points having polar co-ordinates (0, 0), (3, π/2),(3, π/6) are the vertices of an equilateral triangle.
3. Prove that the points (3, π/2), (√3, 0) and (3, 5π/6) form a right-angled triangle.
Answers for the worksheet on distance between the polar co-ordinates are given below to check the exact answers of the above questions.
1. (i) 7 units.
(ii) 2a units.
● Co-ordinate Geometry