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**

**What is Co-ordinate Geometry?****Rectangular Cartesian Co-ordinates****Polar Co-ordinates****Relation between Cartesian and Polar Co-Ordinates****Distance between Two given Points****Distance between Two Points in Polar Co-ordinates****Division of Line Segment****: Internal & External****Area of the Triangle Formed by Three co-ordinate Points****Condition of Collinearity of Three Points****Medians of a Triangle are Concurrent****Apollonius' Theorem****Quadrilateral form a Parallelogram****Problems on Distance Between Two Points****Area of a Triangle Given 3 Points****Worksheet on Quadrants****Worksheet on Rectangular – Polar Conversion****Worksheet on Line-Segment Joining the Points****Worksheet on Distance Between Two Points****Worksheet on Distance Between the Polar Co-ordinates****Worksheet on Finding Mid-Point****Worksheet on Division of Line-Segment****Worksheet on Centroid of a Triangle****Worksheet on Area of Co-ordinate Triangle****Worksheet on Collinear Triangle****Worksheet on Area of Polygon****Worksheet on Cartesian Triangle**

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