Study guides › Level 7 · Geometry

The midpoint of two points

Level 7 · Geometry · for questions like “What is the midpoint of (2, −4) and (8, 6)?”

💡 The idea

The midpoint is exactly halfway: average the x’s, and average the y’s.

midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)

✏️ Worked examples

1. (2, −4) and (8, 6): x = (2 + 8) ÷ 2 = 5 and y = (−4 + 6) ÷ 2 = 1. The midpoint is (5, 1).

2. (−6, 3) and (2, 9): x = −2 and y = 6. The midpoint is (−2, 6).

⚠️ Watch out

• Add, then halve. Halving the difference gives the distance to the middle, not the point.
• Watch the minus signs.

🎯 Try these

1. (0, 0) and (10, 4)
2. (−3, 5) and (7, −1)
3. (4, −8) and (−2, 2)

Answers: 1) (5, 2) 2) (2, 2) 3) (1, −3)

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