IGCSE Math RevisionQuestion 1
Write down the equation of the line parallel to \(y = 3x - 1\) that passes through \((0, 4)\).
Show the worked answer
- Parallel lines have the same gradient, \(3\). The line crosses the \(y\)-axis at \(4\).
Answer: \(y = 3x + 4\)
Cambridge IGCSE Maths (0580) · Topic 3: Coordinate geometry · 3.6, 3.7
Cambridge IGCSE Maths 0580 Parallel and Perpendicular Lines Questions
Parallel and Perpendicular Lines questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
- 9 questions
- 6 Core
- 3 Extended
- 7 non-calculator
- Free, no sign-in
What the syllabus asks
- 3.6 Parallel lines Core
Find the gradient and equation of a line parallel to a given line. - 3.7 Perpendicular lines Extended only
Extended: Find the gradient and equation of a line perpendicular to a given line, including perpendicular bisectors.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
Parallel and Perpendicular Lines questions: Core
For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).
Question 2
Is the line \(y = 2x + 5\) parallel to the line \(2y = 4x - 3\)? Give a reason.
Show the answer and mark scheme
- M1 2y = 4x − 3 gives y = 2x − 1.5
- A1 yes, both have gradient 2
Answer: yes: both have gradient \(2\)
Question 3
Find the equation of the line parallel to \(y = -2x + 5\) that passes through \((3, 1)\).
Show the worked answer
- Gradient \(-2\): \(y = -2x + c\).
- \(1 = -2 \times 3 + c\), so \(c = 7\).
Answer: \(y = -2x + 7\)
Question 4
Which two of these lines are parallel?
\(y = 4x + 1 \qquad y = 1 - 4x \qquad 2y = 8x - 3 \qquad y = 4 + x\)
Show the worked answer
- Gradients: \(4\), \(-4\), \(4\) (since \(y = 4x - 1.5\)) and \(1\).
- The two lines with gradient \(4\) are parallel.
Answer: \(y = 4x + 1\) and \(2y = 8x - 3\)
Question 5
Find the equation of the line parallel to \(y = 3x + 2\) that passes through \((2, 1)\).
Show the answer and mark scheme
- M1 1 = 3 × 2 + c
- A1 y = 3x − 5
Answer: \(y = 3x - 5\)
Question 6
Find the equation of the line parallel to \(y = -\frac{1}{2}x + 4\) that passes through \((4, 5)\).
Show the answer and mark scheme
- M1 5 = −½ × 4 + c
- A1 y = −½x + 7
Answer: \(y = -\frac{1}{2}x + 7\)
Parallel and Perpendicular Lines questions: Extended
Extended content, for Papers 2 and 4. Core students can skip these.
Question 7
Write down the gradient of a line perpendicular to \(y = \frac{2}{3}x + 1\).
Show the worked answer
- Perpendicular gradients multiply to \(-1\): \(\frac{2}{3} \times m = -1\).
- \(m = -\frac{3}{2}\)
Answer: \(-\frac{3}{2}\)
Question 8
Find the equation of the line perpendicular to \(y = 2x - 3\) that passes through \((4, 1)\).
Show the worked answer
- Perpendicular gradient: \(-\frac{1}{2}\).
- \(1 = -\frac{1}{2} \times 4 + c\), so \(c = 3\).
Answer: \(y = -\frac{1}{2}x + 3\)
Question 9
\(A\) is \((1, 2)\) and \(B\) is \((5, 10)\). Find the equation of the perpendicular bisector of \(AB\).
Show the worked answer
- Midpoint of \(AB\): \((3, 6)\). Gradient of \(AB\): \(\frac{8}{4} = 2\).
- Perpendicular gradient: \(-\frac{1}{2}\).
- \(6 = -\frac{1}{2} \times 3 + c\), so \(c = 7.5\).
Answer: \(y = -\frac{1}{2}x + 7.5\)
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Keep going
- Coordinate geometry practice for 0580: more questions, each one marked, tagged Core or Extended
- My mistakes, then a Skill Builder on the skills you missed
- Common mistakes in 0580: what the Cambridge examiner reports say
- Coordinate geometry revision notes and the 0580 formula sheet
- Cambridge IGCSE Maths 0580 past papers, when you are ready for a full paper
Questions students ask
Which Cambridge 0580 papers can test parallel and perpendicular lines?
Parallel and Perpendicular Lines is on both tiers (syllabus 3.6, 3.7), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.
Are these Cambridge past-paper questions?
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
Where can I practise more parallel and perpendicular lines questions?
In the 0580 practice for topic 3 (Coordinate geometry), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.