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Flip to reveal answersWhat is a perpendicular bisector?
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All 8 Flashcards — Perpendicular bisector
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Question
What is a perpendicular bisector?
Answer
The line through the midpoint of a segment, perpendicular to it (negative-reciprocal gradient).
Question
State the three steps to find a perpendicular bisector.
Answer
1) Midpoint of the endpoints. 2) Gradient of the segment, then its negative reciprocal. 3) Substitute the midpoint into y = mx + c.
Question
Midpoint of (x₁, y₁) and (x₂, y₂)?
Answer
((x₁ + x₂)/2, (y₁ + y₂)/2) — average each coordinate.
Question
Which gradient does the bisector use?
Answer
The negative reciprocal of the segment's gradient (flip the fraction and change the sign).
Question
Which point does the bisector pass through?
Answer
The midpoint of the two endpoints — not either endpoint.
Question
What is special about every point on the perpendicular bisector?
Answer
It is equidistant from the two endpoints (the same distance from A as from B).
Question
Perpendicular bisector of A(1, 2) and B(5, 8)?
Answer
Midpoint (3, 5); m_AB = 3/2 → bisector gradient −2/3; y = −2/3 x + 7.
Question
Bisector answer needs general form — what do you do?
Answer
Build y = mx + c first, then clear fractions and move everything to one side: ax + by + d = 0.
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Full study notes for Perpendicular bisector
Topic 2.1 hub
Straight lines
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