Pure · Coordinate geometry
Chapter 1 · 4
The idea
Parallel and perpendicular lines
Parallel lines share a gradient; perpendicular gradients multiply to −1 (the negative reciprocal). Using both — and the perpendicular bisector of a segment — to find equations of lines.
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Pure · Coordinate geometry
Parallel and perpendicular lines
Parallel lines share a gradient; perpendicular gradients multiply to −1 (the negative reciprocal). Using both — and the perpendicular bisector of a segment — to find equations of lines.
Why it works
Parallel: same gradient
Two lines are parallel when they have the same gradient — same steepness, never meeting. So to build a line parallel to a given one, lift its gradient straight off and pair it with the new point.Perpendicular: flip it AND change the sign
Two lines are perpendicular when their gradients multiply to :That second form, the negative reciprocal, is the one you use in practice — read it back as flip it and change the sign, both steps.
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The rest of the explanation, plus 3 worked examples you step through move by move.
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