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

What is the sum of the first 10 positive even numbers?

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If a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?

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If x^2 - 6x + 9 = 0, what is the value of x?

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What is the cube of 4?

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A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

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What is the slope of a line passing through the points (2, 3) and (4, 7)?

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The probability of getting an even number when rolling a die is:

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If a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

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A rectangle has a length of 10 cm and a width of 5 cm. What is the diagonal of the rectangle?

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If the length of a rectangle is doubled and the width is halved, what is the change in area?

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