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

If the sum of the squares of two consecutive positive integers is 365, what are the integers?

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If the sum of three consecutive integers is 72, what are the integers?

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If the cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

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

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What is the remainder when 5^100 is divided by 3?

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If the sum of the angles of a polygon is 1080°, how many sides does the polygon have?

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If the radius of a circle is 7 cm, what is its circumference?

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If a+b = 10 and ab = 21, what is the value of a^3 + b^3?

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If a right triangle has legs of 9 cm and 12 cm, what is the length of the hypotenuse?

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