Cambridge O Level Mathematics (Syllabus D) · Syllabus 4024 · Coordinate Geometry
Perpendicular Lines
What is Perpendicular Lines?
Two straight lines that cross at an angle of 90 degrees. When both have a defined gradient, the product of their gradients is minus one, so each gradient is the negative reciprocal of the other: the fraction is inverted and its sign is changed. The one perpendicular pair this rule cannot describe is a horizontal line, of gradient zero, meeting a vertical line, whose gradient is undefined. The perpendicular bisector of a line segment is the line perpendicular to it that also passes through its midpoint.
This definition is part of the Coordinate Geometry chapter in Cambridge O Level Mathematics (Syllabus D).
Common mistakes with Perpendicular Lines
- “Parallel means the gradients are negative reciprocals.” Swapped Parallel lines have equal gradients. Perpendicular lines have negative reciprocal gradients. The swap is a costly one, because it produces a tidy-looking answer that is nevertheless a completely different line.
Last reviewed Syllabus 2025-2027