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A Center Off the Origin

Part of the Transformations & Constructions section of Coddy's Geometry journey. Lesson 14 of 61.

The center does not have to be the origin. Work from the center instead: find the step from the center to the point, turn that step, then add it back to the center.

$P turned a quarter turn counterclockwise about the center C$

Turn P(5, 2) a quarter turn counterclockwise about C(1, 1). From C to P is the step ⟨4, 1⟩. A quarter turn counterclockwise turns it into ⟨-1, 4⟩, as the rule (-y, x) says. Add that to C: P' = (1 - 1, 1 + 4) = (0, 5). Both arms, CP and CP', have the same length, as they must.

Challenge

Turn triangle ABC 90° clockwise about the point K(1, 2). Drag A', B' and C' into place, then press Check.

Try it yourself

$Move the shape onto its target$

Move the shape onto its target

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Transformations & Constructions

1Translations

Sliding a Shape Draw the Image Image Coordinates The Translation Rule Recap: Translations

4Combining Moves

One Move, Then Another Order Matters Two Mirrors Name the Move Recap: Combining Moves

7Drawing on Squared Paper

Lengths by Pythagoras Perpendicular Steps Squares by Area Right Triangles by Area Midpoints on the Grid Recap: Squared Paper

10Perpendiculars and Parallels

Perpendicular From a Point Perpendicular at a Point Parallel Through a Point Tools You Have Earned Recap: Parallels

3Rotations

Turning About a Point The Half Turn Quarter-Turn RulesA Center Off the OriginRecap: Rotations

6Symmetry

Lines of Symmetry Rotational Symmetry Regular Polygons Symmetry Is a Move Recap: Symmetry

9Bisectors

The Perpendicular Bisector The Midpoint Bisecting an Angle Half of 60°Recap: Bisectors

12Final Challenges

Final: Footprints Final: Two Moves, One Rule Final: Mirror on the Grid Final: The Fair Well Final: The Tangent Road