Knowledge Organiser: Parallel and Perpendicular Lines
Part of Parallel & Perpendicular · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Parallel and Perpendicular Lines within Parallel & Perpendicular for GCSE Mathematics. Revise Parallel & Perpendicular in Graphs for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 10 of 10 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 10 of 10
Practice
14 questions
Recall
12 flashcards
Knowledge Organiser: Parallel and Perpendicular Lines
Key Terms
- Parallel lines: Lines that never meet; they have the same gradient
- Perpendicular lines: Lines that meet at exactly 90°
- Negative reciprocal: For gradient m, the perpendicular gradient is −1 ÷ m
- Gradient product: Two perpendicular lines satisfy m₁ × m₂ = −1
Must-Know Facts
- Parallel lines have identical gradients but different y-intercepts
- Perpendicular gradients multiply to give −1 (they are negative reciprocals)
- To find a parallel line through a point: use same m, substitute point to find c
- To find a perpendicular line through a point: use m₂ = −1 ÷ m₁, then find c
- Horizontal (m = 0) and vertical (undefined m) lines are always perpendicular to each other
- If m = 2, the perpendicular gradient is −½; if m = −3, it is ⅓
Key Formulas
- Parallel condition: m₁ = m₂
- Perpendicular condition: m₁ × m₂ = −1
- Perpendicular gradient: m₂ = −1 ÷ m₁
- Equation of new line: substitute m and a given point into y = mx + c to find c
Common Mistakes
- Perpendicular gradient = negative reciprocal: If m = 3, perpendicular gradient is −⅓ (flip and negate) — not just −3
- Parallel lines have the SAME gradient: A parallel line through a different point has the same m but a different c
- Not finding c: After finding the gradient, always substitute the given point to find the y-intercept c
- m₁ × m₂ = −1 check: Verify perpendicularity by multiplying the two gradients — result must be −1 exactly
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Practice Questions for Parallel & Perpendicular
Which of the following is true about two parallel straight lines?
Explain why a horizontal line and a vertical line are always perpendicular to each other. Your explanation must refer to gradients.
Quick Recall Flashcards
14 questions on Parallel & Perpendicular — practise free
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