Midpoint and length of a line Edexcel International GCSE Mathematics A revision
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In plain words
Given two points you can find the point exactly halfway between them, and how far apart they are. Halfway is just the average. The distance is Pythagoras: the line is the long side of a right-angled triangle.
Three things to know
- Midpoint: average the x-coordinates and average the y-coordinates. ((x₁ + x₂)/2, (y₁ + y₂)/2).
- Length: √((x₂ − x₁)² + (y₂ − y₁)²).
- Sketch the two points and the right-angled triangle between them if you're unsure.
Worked example
A is (1, 2) and B is (7, 10). Find the midpoint and the length of AB.
- Midpoint: ((1 + 7)/2, (2 + 10)/2) = (4, 6).
- Differences: 7 − 1 = 6 across and 10 − 2 = 8 up.
- Length = √(6² + 8²) = √100 = 10.
Tips and tricks
- Midpoint: add and halve. Length: subtract, square, add, root.
- Squaring a negative difference gives a positive number, so the order of subtraction doesn't matter for length.
It lands in your notebook with its questions as flashcards.
Midpoint and length of a line: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is the midpoint of (0, 0) and (4, 6)?
Halve each coordinate.
What is the length of the line from (0, 0) to (3, 4)?
√(9 + 16).
What is the midpoint of (1, 5) and (3, 9)?
(1 + 3)/2 and (5 + 9)/2.
Which theorem is used to find the length of a line between two points?
The line is the hypotenuse of a right-angled triangle.
What is the length of the line from (2, 1) to (2, 9)?
It is vertical: 9 − 1.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 8 marks. Write your answers on paper, then check them.
Midpoint and length of a line
Edexcel International GCSE Mathematics A 4MA1 · 8 marks · papermunch.org
Name ______________________________ Date ______________
Find the midpoint of the line joining (2, 3) and (8, 7).[2]
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(5, 5).
Find the length of the line joining (0, 0) and (5, 12).[3]
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13. √(25 + 144).
Find the length of the line joining (−1, 2) and (2, 6).[3]
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5. √(3² + 4²).
Answers: Midpoint and length of a line
- 1. (5, 5).
- 2. 13. √(25 + 144).
- 3. 5. √(3² + 4²).