Quarter-Turn Rules
Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 13 of 61.
A quarter turn about the origin also has a rule. Turning 90° counterclockwise sends (x, y) to (-y, x): the coordinates swap, and the new x takes a minus sign.
Check it on P(4, 1), which is 4 right and 1 up. A quarter turn counterclockwise points that step up and to the left: 1 left and 4 up, which is P'(-1, 4). The rule agrees: (-y, x) = (-1, 4). For Q(4, 3) it gives Q'(-3, 4).
A quarter turn clockwise undoes the counterclockwise one, so its rule runs the other way. Work it out by turning one easy point, such as (1, 0), and seeing where it goes.
Challenge
Triangle ABC has been turned about the origin onto the image drawn on the grid. Write the rule for that turn, then press Check.
Try it yourself
Move the shape onto its target
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 Triangle3Rotations
Turning About a PointThe Half TurnQuarter-Turn RulesA Center Off the OriginRecap: Rotations