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Perpendicular Lines

Part of Parallel & Perpendicular — GCSE Mathematics

This key facts covers 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 3 of 9 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 3 of 9

Practice

14 questions

Recall

12 flashcards

Perpendicular Lines

  • Definition: Lines that meet at 90° (right angles)
  • Key Property: Gradients multiply to give -1
  • If one gradient is m, the other is -1/m
  • Symbol: ⊥ (e.g., L₁ ⊥ L₂)
  • Special case: Horizontal and vertical lines are always perpendicular

Keep building this topic

Read this section alongside the surrounding pages in Parallel & Perpendicular. That gives you the full topic sequence instead of a single isolated revision point.

Parallel LinesParallel and Perpendicular LinesTrain Tracks and Right AnglesThe Gradient Rules

Practice Questions for Parallel & Perpendicular

Which of the following is true about two parallel straight lines?

  • A. They have the same gradient but different y-intercepts
  • B. Their gradients multiply to give -1
  • C. They have the same gradient and the same y-intercept
  • D. One gradient is the negative of the other
1 markfoundation

Explain why a horizontal line and a vertical line are always perpendicular to each other. Your explanation must refer to gradients.

2 marksstandard

Quick Recall Flashcards

What is the gradient rule for parallel lines?
Parallel lines have equal gradients. If L1 has gradient m1 and L2 has gradient m2, then L1 || L2 means m1 = m2.
What is the gradient rule for perpendicular lines?
Perpendicular lines have gradients that multiply to -1. If L1 perp L2 then m1 x m2 = -1.

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Parallel and Perpendicular Lines