Transformations Cheat Sheet - Reflections, Translations, Dilations, Rotations

Sep 15, 2026

Uploaded by Kyle

Concise cheat sheet for geometric transformations in a coordinate plane, defining reflections, translations, dilations, and rotations with core properties such as whether each transformation is isometric and whether it preserves orientation. Includes coordinate-plane rules for common reflection axes (x-axis, y-axis, y=x, and through the origin), translation shifts by (h,k), dilation scaling from the origin and from non-origin points, and rotation mappings for standard angles in clockwise and counter-clockwise directions.

LanguageEnglish

CategoryExam

FormatPDF

Pages1

Reading Time3 min

AccessFree to download

Reflections

Translation (Slide/Shift)

Dilations (Scale)

Rotations (Turn)

FAQs

How do reflections change points on the coordinate plane?

Reflections swap coordinates based on the chosen line: over the x-axis (x,y)->(x,−y), over the y-axis (x,y)->(−x,y), over y=x (x,y)->(y,x), and through the origin (x,y)->(−x,−y).

How are translations represented using coordinate changes?

Translations move points by horizontal and vertical shifts: (x,y)->(x±h,y±k), where h and k represent the amounts of left/right and up/down movement. Left implies h is negative and down implies k is negative.

What coordinate rule applies to rotations by standard angles?

For counter-clockwise 90°: (x,y)->(−y,x); for counter-clockwise 180°: (x,y)->(−x,−y); and for counter-clockwise 270°: (x,y)->(y,−x), with corresponding clockwise mappings also listed.

Sep 15, 2026

Uploaded by Kyle