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MathidiaMathematics Academy
Pythagoras and trigonometry
Lesson 47 of 75
Easy practice

Distance between coordinates

Objective. Use Pythagoras to find distance on a coordinate grid.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

The distance between two coordinates on a grid can be found using Pythagoras' theorem by treating the horizontal and vertical gaps between the points as the two shorter sides of a right-angled triangle. To find the distance between (x₁, y₁) and (x₂, y₂), calculate the horizontal difference (x₂ − x₁) and the vertical difference (y₂ − y₁), square both, add them, then take the square root of the total. For example, the distance between (1, 2) and (4, 6) uses differences of 3 and 4, giving √(3² + 4²) = √25 = 5. This method works for any pair of coordinates, regardless of which quadrant they lie in, as long as the differences are squared to remove negative signs.

Worked example

Find the distance between the coordinates (2, 3) and (7, 15).

2 … 3
Coordinate grid with the line 2 … 3
  1. 1Find the horizontal difference: 7 − 2 = 5.
  2. 2Find the vertical difference: 15 − 3 = 12.
  3. 3Square and add: 5² + 12² = 25 + 144 = 169.
  4. 4Take the square root: √169 = 13.

Answer: 13 units

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Practice

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Common mistake. Pupils sometimes forget to square the coordinate differences before adding them, simply adding the raw differences together instead, which ignores the Pythagorean relationship entirely. Always square each difference before adding and then take the square root.

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