Study guides › Level 6 · Master

Distance between two points

Level 6 · Master · for questions like “How far apart are (1, 2) and (4, 6)?”

💡 The idea

Draw the straight line between the points and make it the longest side of a right triangle. The other two sides are how far across and how far up or down. Then use Pythagoras.

distance = √(across² + up²)

🪜 The steps

1. Across: the difference between the x’s.
2. Up or down: the difference between the y’s.
3. Square both, add them, then take the square root.

✏️ Worked examples

1. (1, 2) to (4, 6): across 3, up 4. √(9 + 16) = √25 = 5.

2. (−2, 1) to (10, 6): across 12, up 5. √(144 + 25) = √169 = 13.

⚠️ Watch out

• Negatives: from −2 to 10 is 12 across, not 8.
• Square before adding, then take the square root at the end.

🎯 Try these

1. (0, 0) to (6, 8)
2. (2, −1) to (10, 14)
3. (−3, −3) to (4, 21)

Answers: 1) 10 2) 17 3) 25

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.