Perpendicular Steps
Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 32 of 61.
A segment on squared paper has a step: so many across, so many up. To go at right angles to it, turn the step a quarter turn. From the Rotations chapter, a quarter turn sends ⟨a, b⟩ to ⟨-b, a⟩: swap the two numbers and change the sign of one.
PQ goes 3 across and 1 up. Turned a quarter, that is 1 left and 3 up, so PR is perpendicular to PQ. The reverse step, 1 right and 3 down, is perpendicular too. A step that is a multiple, like ⟨6, 2⟩, points the same way, so reduce it first: ⟨6, 2⟩ is twice ⟨3, 1⟩.
Challenge
C lies on the segment AB. Draw a segment through C perpendicular to AB, then press Check.
Try it yourself
Draw it on squared paper
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