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Maths Olympiad · topic 28 of 33 · free

Coordinates and distance — Maths Olympiad practice

A point (x, y) is x across and y up. The distance between two points is the long side of a right triangle whose short sides are the differences in x and in y. Olympiad questions often use Pythagorean triples like 3, 4, 5 and 5, 12, 13 so the answer is a whole number.

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How to solve it

Across, up, Pythagoras — “the gap in x and the gap in y are the two short sides of a right triangle”

  1. Distance: across = difference of the x values, up = difference of the y values; distance = √(across² + up²).
  2. Midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2).
  3. Quadrants by signs: (+, +) first, (−, +) second, (−, −) third, (+, −) fourth.

Use it for: Graph, map and coordinate geometry questions in Class 8–10 Olympiad papers.

Worked example: What is the distance between the points (1, 2) and (7, 10)? → 10

  1. Across: 7 − 1 = 6. Up: 10 − 2 = 8.
  2. Distance = √(6² + 8²) = √(36 + 64) = √100 = 10.

Check: 6, 8, 10 is the 3, 4, 5 triangle doubled, and 10 × 10 = 100 ✓

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✓ Written and checked by the TalentJR team · Updated 13 Oct 2026 · How we make our lessons

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🖨️ Coordinate Geometry Worksheet for Maths Olympiad

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