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 LCM of 12 and 15 is:

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If x:y = 2:3 and z:y = 4:3, what is x:z?

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What is the cube of 4?

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A man rows downstream at 6 km/h and upstream at 4 km/h. What is the speed of the stream?

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A number is increased by 20% and then decreased by 10%. What is the net change?

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The area of an equilateral triangle with side length 6 cm is:

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A car covers a distance of 150 km in 2.5 hours. What is its average speed?

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What is the sum of the first 20 odd numbers?

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If a = 2 and b = 3, what is the value of (a^2 + b^2)?

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A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

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