# Worksheet on Distance Between the Polar Co-ordinates

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

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