垂線(すいせん)

Compound of 垂(すい) ('hang down; drop vertical') and 線(せん) ('line'). The standard Japanese mathematical term for a perpendicular line. Essential vocabulary in middle- and high-school geometry and in any technical field involving drawing, engineering, or physics.

Usage

• Typical verb patterns describe how perpendiculars are constructed in diagrams:
• 垂線(すいせん)を引(ひ)く: 'draw a perpendicular' — the most general phrase.
• 垂線(すいせん)を下(お)ろす: 'drop a perpendicular' — when the perpendicular goes from a point down to a line or plane.
• 垂線(すいせん)を立(た)てる: 'erect a perpendicular' — when the perpendicular goes up from a line or plane at a given point.
• The foot of the perpendicular — where it meets the reference line — is called the 垂線(すいせん)の足(あし) ('foot of the perpendicular').
• In everyday non-mathematical contexts, to describe something as perpendicular to something else, speakers usually say 垂直(すいちょく) or 直角(ちょっかく) rather than 垂線(すいせん).

Common collocations

• 垂線(すいせん)を引(ひ)く: to draw a perpendicular
• 垂線(すいせん)を下(お)ろす: to drop a perpendicular
• 垂線(すいせん)を立(た)てる: to erect a perpendicular
• 垂線(すいせん)の足(あし): the foot of the perpendicular
• 垂線(すいせん)の長(なが)さ: the length of the perpendicular (i.e., the distance from the point to the line)

Similar words

• 垂直(すいちょく): vertical; perpendicular — the adjectival/general property; used in everyday descriptions like 垂直(すいちょく)に立(た)つ ('to stand upright').
• 直角(ちょっかく): right angle — the angle formed between a perpendicular and the reference line.
• 平行線(へいこうせん): parallel line — the opposite geometric concept.
• 法線(ほうせん): normal line — the perpendicular to a curve or surface at a given point; a more advanced technical term used in calculus and physics.
• 直線(ちょくせん): straight line — the general term, not specifying any angle relationship.