Topic Details (Notes format)

How to Use the Distance Formula (Coordinate Geometry)

Subject: Mathematics

Book: Maths Mastery

In a 2D coordinate plane, the distance between two points (x₁, y₁) and (x₂, y₂) is given by √[(x₂ – x₁)² + (y₂ – y₁)²]. For instance, the distance between (2, 3) and (6, 7) is √[(6 – 2)² + (7 – 3)²] = √(4² + 4²) = √32 = 4√2. Derived from the Pythagorean Theorem, the distance formula is pivotal in map reading, robotics pathfinding, or designing game environments. Familiarity with it ensures you can measure and compare positional relationships quickly and accurately in a variety of analytical tasks.

Practice Questions

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If x^3 - 3x^2 + 4 = 0, what is one root of the equation?

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A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

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If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

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The ratio of two numbers is 3:5, and their sum is 64. What are the numbers?

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The perimeter of a rectangle is 40 cm, and its length is 12 cm. What is its width?

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