The midpoint of a line segment is halfway between its ends. Add the x-coordinates and halve, then add the y-coordinates and halve. The midpoint of (−3, 6) and (4, 12) is (0.5, 9).
The length of a line segment comes from Pythagoras' theorem. Find the change in x and the change in y, square them, add and take the square root. From (1, 5) to (6, −1): changes 5 and −6, so the length is √(25 + 36) = √61 ≈ 7.8.
Worked example
Find the length of the segment from A(0, −4) to B(6, −12).
- Change in x: 6. Change in y: −8.
- √(6² + 8²) = √100.
Answer:10
Key words
- midpoint
- the point halfway along a segment
- line segment
- part of a line between two points
- distance formula
- √((x₂ − x₁)² + (y₂ − y₁)²)
Practise this
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Common Core-referenced: HSG-GPE.B.6, HSG-GPE.B.7