Transformations Graphic Organizer PDF

A blank box each for translation, reflection, rotation and dilation: sketch the move, then say what changes.

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Name:Date:TranslationSketch a figure and its image, then say what changesReflectionSketch a figure and its image, then say what changesRotationSketch a figure and its image, then say what changesDilationSketch a figure and its image, then say what changesWhich three keep the size and shape?
Transformations graphic organizer: four boxes to sketch and describe A box each for translation, reflection, rotation and dilation, with room for a sketch over lines, and a box at the foot that asks which three keep a figure's size and shape.
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How it works

This transformations graphic organizer sets the four moves side by side, so the difference that matters shows: three of them keep a figure's size and shape, and one can change its size.

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Draw what each move needs

A translation needs a distance and a direction. A reflection needs a line. A rotation needs a center and an angle, and a dilation needs a center and a scale factor. Have students draw these into the sketch itself: an arrow for the slide, the mirror line, a dot for the center.

Congruent or similar

In the Common Core standards for 8th grade, two figures are congruent when a sequence of rotations, reflections and translations takes one to the other. Put a dilation in the sequence and they are similar. The sheet for two moves in a row ends on that question.

  • Label the image with prime marks: A goes to A′ and B to B′. It shows which corner went where.
  • A scale factor greater than 1 enlarges a figure. A scale factor between 0 and 1 shrinks it.

Questions and answers

What are the four types of transformations?

Translation, reflection, rotation and dilation. A translation slides a figure, a reflection flips it over a line, a rotation turns it about a point, and a dilation enlarges or shrinks it from a center.

What is a rigid transformation?

One that keeps the distance between every pair of points, so a figure keeps its size and shape. Translations, reflections and rotations are rigid. A dilation that enlarges or shrinks a figure is not.

What is the rule for a 90 degree rotation?

Turning counterclockwise about the origin, the point (x, y) goes to (−y, x), so (2, 3) goes to (−3, 2). Clockwise, it goes to (y, −x). A 180° rotation sends (x, y) to (−x, −y) either way.

What grade are transformations taught?

In the Common Core standards they are 8th grade geometry: students verify the properties of rotations, reflections and translations, and describe the effect of all four on figures using coordinates. They return in high school geometry.

All 11 organizers

A box for each transformation 3

  • One transformation in four boxes A whole page for one transformation, with its name in the middle: what it does, what it needs, its rule with coordinates and a drawing.
  • Transformation exit slips, two to a page Two half sheets with a cut line between them: name one transformation, say what changed and what stayed the same.
  • Transformations graphic organizer: four boxes to sketch and describe A box each for translation, reflection, rotation and dilation, with room for a sketch over lines, and a box at the foot that asks which three keep a figure's size and shape.

Charts and rules 3

  • Coordinate rules chart Eight moves of a point, from a translation to a dilation. Write where (x, y) goes, then try the rule on the point (2, 3).
  • Transformations chart: what it does, what it needs, what stays the same A sideways page with a column for each transformation and three rows of open boxes.
  • Which transformation? Eight statements to tick Tick every transformation a statement is true of. Some rows take one tick and some take more.
Show all 11 organizers (5 more)

Grids and sequences 2

  • Four grids to sketch on Four coordinate grids from −6 to 6, two by two, every second line numbered: one for each transformation.
  • Two transformations in a row Three boxes joined by arrows for the figure, its image after the first move and its image after the second, with lines above for the two moves and a box that asks whether the last image is congruent or similar to the figure.

Sample and answer keys 3

  • Answer key: coordinate rules chart The eight rules written in, each tried on the point (2, 3).
  • Answer key: eight statements The tick chart with an X in each right box. Statement 1 is true of three transformations and statement 6 of all four.
  • Sample transformations organizer, filled in The four boxes written in and the sketches left to draw.

How this list was compiled: Our own layouts and wording; no publisher's organizer is copied. What each transformation does and what it keeps were checked against the Wikipedia articles Translation (geometry), Reflection (mathematics), Rotation (mathematics), Homothety, Rigid transformation and Similarity (geometry) and the grade 8 geometry standards and glossary of the Common Core State Standards for Mathematics, read October 13, 2026. The coordinate rules and both answer keys were worked out twice. Licence: own work

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