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.

Answers:

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

11 and 12 Grade Math 

From Worksheet on Distance Between the Polar Co-ordinates to HOME PAGE