Parallel and perpendicular lines Cambridge IGCSE Mathematics (9–1) revision
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In plain words
Two lines that never meet are parallel: they are equally steep. Two that cross at a right angle are perpendicular, and their gradients are linked in a neat way: turn one upside down and change its sign.
Three things to know
- Parallel lines have the same gradient.
- Perpendicular lines have gradients that multiply to −1. If one is m, the other is −1/m: for 2, it's −1/2; for 3/4, it's −4/3.
- To find the equation, get the gradient this way, then use a point to find c.
Worked example
Find the equation of the line perpendicular to y = 2x + 1 that passes through (4, 3).
- The gradient of the given line is 2, so the perpendicular gradient is −1/2.
- y = −½x + c. Put in (4, 3): 3 = −2 + c, so c = 5.
- y = −½x + 5.
Tips and tricks
- Perpendicular: flip the fraction and change the sign. Do both.
- Check: 2 × (−1/2) = −1.
It lands in your notebook with its questions as flashcards.
Parallel and perpendicular lines: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
Which line is parallel to y = 2x + 1?
It has the same gradient, 2.
A line has gradient 3. What is the gradient of a perpendicular line?
3 × (−1/3) = −1.
What do the gradients of two perpendicular lines multiply to give?
That is the test for a right angle between them.
A line has gradient −1/2. What is the gradient of a perpendicular line?
Flip it and change the sign.
Which line is perpendicular to y = x?
Gradients 1 and −1 multiply to −1.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 6 marks. Write your answers on paper, then check them.
Parallel and perpendicular lines
Cambridge IGCSE Mathematics (9–1) 0980 · 6 marks · papermunch.org
Name ______________________________ Date ______________
Write down the equation of the line parallel to y = 3x + 2 that passes through (0, −4).[2]
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y = 3x − 4.
A line has gradient 4. Write down the gradient of a line perpendicular to it.[1]
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−1/4.
Find the equation of the line parallel to y = 2x − 5 that passes through (1, 6).[3]
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y = 2x + 4. 6 = 2 + c.
Answers: Parallel and perpendicular lines
- 1. y = 3x − 4.
- 2. −1/4.
- 3. y = 2x + 4. 6 = 2 + c.