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

The simple interest on Rs. 4000 at 5% per annum for 2 years is:

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What is the square root of 0.25?

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If x² - 9x + 18 = 0, what are the roots of the equation?

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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

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If a = 4 and b = 5, what is the value of (a+b)^2?

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The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

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