Parallel & perpendicular lines
AQA GCSE Maths revision on Parallel & perpendicular lines. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 17 practice questions on this topic.
Sample questions (3 of 17)
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Question 1
If two lines are parallel, what must be true about their gradients?
- A) They are identical
- B) They are negative reciprocals
- C) They sum to zero
- D) They have opposite signs
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Answer: They are identical
For two lines to never intersect, their rate of change must be the same. If one line rises more steeply than the other, they will eventually meet at a point. Therefore, the gradient m1 must equal m2 for parallel lines.
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Question 2
A student claims that any two lines with the same y-intercept must be parallel. Why is this incorrect?
- A) The y-intercept does not affect parallelism
- B) Lines with the same intercept must be perpendicular
- C) Lines with the same intercept will intersect at that point
- D) Parallel lines cannot have a y-intercept
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Answer: Lines with the same intercept will intersect at that point
Parallel lines must have different y-intercepts to remain separate. If two lines share the same y-intercept but have different gradients, they are intersecting lines, not parallel ones.
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Question 3
What is the relationship between the gradients of two perpendicular lines?
- A) They are the same
- B) They are negative reciprocals
- C) They are equal to one
- D) They are additive inverses
Show answer
Answer: They are negative reciprocals
If a line has a gradient of m, its perpendicular counterpart must have a gradient of -1/m. This ensures the product of their gradients is always -1, creating a right angle.
Want to test yourself on the remaining cards for this topic?
14 more questions on Parallel & perpendicular lines — plus mistakes tracking and spaced repetition across the whole Maths spec.