1.
perpendicular line; perpendicular (from a point to a line or plane)
In geometry, a straight line that meets another line or plane at a right angle, especially one drawn from a given point perpendicular to a reference line or plane. Standard terminology in school mathematics and technical drawing.
垂線を引く。
To draw a perpendicular line.
点Aから直線BCに垂線を下ろす。
Drop a perpendicular from point A to line BC.
二つの平面が交わる直線に垂線を立てて角度を求めた。
I set up a perpendicular to the line where the two planes meet and found the angle.
Compound of 垂 ('hang down; drop vertical') and 線 ('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:
- 垂線を引く: 'draw a perpendicular' — the most general phrase.
- 垂線を下ろす: 'drop a perpendicular' — when the perpendicular goes from a point down to a line or plane.
- 垂線を立てる: '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 垂線の足 ('foot of the perpendicular').
- In everyday non-mathematical contexts, to describe something as perpendicular to something else, speakers usually say 垂直 or 直角 rather than 垂線.
COMMON COLLOCATIONS:
- 垂線を引く: to draw a perpendicular
- 垂線を下ろす: to drop a perpendicular
- 垂線を立てる: to erect a perpendicular
- 垂線の足: the foot of the perpendicular
- 垂線の長さ: the length of the perpendicular (i.e., the distance from the point to the line)
SIMILAR WORDS:
- 垂直: vertical; perpendicular — the adjectival/general property; used in everyday descriptions like 垂直に立つ ('to stand upright').
- 直角: right angle — the angle formed between a perpendicular and the reference line.
- 平行線: parallel line — the opposite geometric concept.
- 法線: 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: straight line — the general term, not specifying any angle relationship.