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All 10 Flashcards — Parallel & perpendicular
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Question
When are two lines parallel?
Answer
When they have the same gradient: m₁ = m₂ (with different y-intercepts).
Question
When are two lines perpendicular?
Answer
When their gradients multiply to −1: m₁m₂ = −1, i.e. m₂ = −1/m₁.
Question
How do you get the perpendicular gradient?
Answer
Take the negative reciprocal — flip the fraction and change the sign. E.g. ⅔ → −3/2.
Question
Perpendicular gradient of 5?
Answer
Write 5 as 5/1; the perpendicular gradient is −1/5.
Question
How do you find a line through a point parallel to a given line?
Answer
Use the SAME gradient, then point–gradient form y − y₁ = m(x − x₁).
Question
How do you find a line through a point perpendicular to a given line?
Answer
Use the negative-reciprocal gradient, then point–gradient form.
Question
What is a perpendicular bisector?
Answer
The line through the midpoint of a segment, perpendicular to it (negative-reciprocal gradient).
Question
Midpoint of (x₁, y₁) and (x₂, y₂)?
Answer
((x₁ + x₂)/2, (y₁ + y₂)/2) — average each coordinate.
Question
What is a normal to a curve?
Answer
The line perpendicular to the tangent at a point; its gradient is −1/(tangent gradient). Used in calculus.
Question
Why doesn't m₁m₂ = −1 work for horizontal & vertical lines?
Answer
They are perpendicular, but a vertical line (x = a) has no gradient, so the product rule can't be applied — state it separately.
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Full study notes for Parallel & perpendicular
Topic 2.1 hub
Straight lines
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