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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
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