Perpendicular From a Point
Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 47 of 61.
To drop a perpendicular from a point R to a line, use two points of the line as circle centers. The circle about X through R and the circle about Y through R cross at R and at a second point R', on the other side of the line. The line RR' is the perpendicular.
Why does it work? X is as far from R as from R', since both are on the circle about X. Y is too. Two points that are each equally far from R and R' fix the perpendicular bisector of RR', so the line XY is that bisector, and RR' crosses it at right angles. The shape XRYR' is a kite folded along XY.
Challenge
Construct the line through P perpendicular to the line AB, then press Check.
Try it yourself
Construct it with a compass and straightedge
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Transformations & Constructions
7Drawing on Squared Paper
Lengths by PythagorasPerpendicular StepsSquares by AreaRight Triangles by AreaMidpoints on the GridRecap: Squared Paper10Perpendiculars and Parallels
Perpendicular From a PointPerpendicular at a PointParallel Through a PointTools You Have EarnedRecap: Parallels5Dilations
Scaling From a CenterShrinking a ShapeDilating About a PointNegative Scale FactorsRecap: Dilations8Compass and Straightedge
Circles Keep DistancesWhy the Sides MatchAngles You BuiltA 60° AngleRecap: Equilateral Triangle