Transformation Vocabulary Worksheet

Press Print worksheet to match twelve transformation terms, from translation and reflection to scale factor, to their meanings.

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NameDateMade at homeroomtools.comDraw a line from each one on the left to its partner on the right.Transformation vocabularytransformationtranslationreflectionrotationdilationimagepre-imagerigid transformationline of reflectioncenter of rotationangle of rotationscale factorthe point that a figure turnsaroundthe figure after it has been movedor resizedthe figure before atransformation is appliedthe number that multiplies eachlength in a dilationa flip to the other side of a line,like in a mirrora transformation that keepsevery distance the samea resizing: every length ismultiplied by one numberhow far a figure turns, measuredin degreesa turn of every point through thesame angle about a centerthe mirror line that a figure isflipped acrossa slide with no turning and nochange of sizea rule that tells where each pointof a figure goes
NameDateMade at homeroomtools.comDraw a line from each one on the left to its partner on the right.Transformation vocabularyAnswer keytransformationtranslationreflectionrotationdilationimagepre-imagerigid transformationline of reflectioncenter of rotationangle of rotationscale factorthe point that a figure turnsaroundthe figure after it has been movedor resizedthe figure before atransformation is appliedthe number that multiplies eachlength in a dilationa flip to the other side of a line,like in a mirrora transformation that keepsevery distance the samea resizing: every length ismultiplied by one numberhow far a figure turns, measuredin degreesa turn of every point through thesame angle about a centerthe mirror line that a figure isflipped acrossa slide with no turning and nochange of sizea rule that tells where each pointof a figure goes
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All 36 terms

The four transformations 12

  • angle of rotation How far a figure turns, measured in degrees. A quarter-turn has an angle of rotation of 90°.
  • center of rotation The point that a figure turns around. The pin at the middle of a clock face is the center of rotation of its hands.
  • dilation A resizing: every length is multiplied by one number. A dilation by 3 from the origin takes (1, 2) to (3, 6).
  • image The figure after it has been moved or resized. When triangle ABC is reflected onto triangle A′B′C′, triangle A′B′C′ is the image.
  • line of reflection The mirror line that a figure is flipped across. A point and its image lie the same distance from the line of reflection, on opposite sides of it.
  • pre-image The figure before a transformation is applied. When triangle ABC is reflected onto triangle A′B′C′, triangle ABC is the pre-image.
  • reflection A flip to the other side of a line, like in a mirror. Reflecting (3, 2) over the x-axis gives (3, −2). A reflection is also called a flip.
Show all 36 terms (29 more)

The four transformations, continued

  • rigid transformation A transformation that keeps every distance the same. Translations, reflections and rotations are rigid transformations. A dilation by 2 is not, because it doubles every distance.
  • rotation A turn of every point through the same angle about a center. A rotation of 90° counterclockwise about the origin takes (3, 2) to (−2, 3). A rotation is also called a turn.
  • scale factor The number that multiplies each length in a dilation. A scale factor of 2 doubles every length, and a scale factor of 1/2 halves it.
  • transformation A rule that tells where each point of a figure goes. A translation, a reflection, a rotation and a dilation are each a transformation.
  • translation A slide with no turning and no change of size. Moving every point 3 units right and 2 units up is a translation. A translation is also called a slide.

Symmetry and similarity 12

  • asymmetric Having no symmetry at all. The capital letter F is asymmetric: no fold and no part turn matches it to itself.
  • congruent Able to fit exactly on top of each other. Two squares with sides of 5 cm are congruent: the same shape and the same size.
  • corresponding In the matching position in two figures. If triangle ABC is similar to triangle DEF, side AB and side DE are corresponding sides.
  • enlargement A dilation with a scale factor greater than 1. A scale factor of 3 gives an enlargement: each side becomes 3 times as long.
  • fixed point Any point that a transformation leaves where it was. In a rotation about the origin, the origin is a fixed point.
  • line of symmetry A fold line whose two sides are mirror images. A square has 4 lines of symmetry.
  • point symmetry Each point has a partner directly across the center. On a flat page, a figure with point symmetry fits onto itself after a half-turn.
  • reduction A dilation with a scale factor between 0 and 1. A scale factor of 1/2 gives a reduction: each side becomes half as long.
  • rotational symmetry Fitting onto itself when turned part of the way around. An equilateral triangle fits onto itself after a third of a full turn, 120°.
  • similar Alike in shape, though one may be larger. Every square is similar to every other square, whatever their sizes.
  • symmetry Balance: parts that match across a line or about a point. A square has symmetry: its left half matches its right half.
  • tessellation A pattern of shapes that fit together with no spaces. Equilateral triangles, squares and regular hexagons can each make a tessellation without any other shape.

Describing the move 12

  • clockwise Turning the way a clock's hands go around. From the 12 to the 3 on a clock face, the minute hand turns 90° clockwise.
  • composition One transformation carried out after another. A reflection followed by a rotation is a composition of two transformations.
  • counterclockwise The reverse of clockwise: the positive turning direction. A rotation of 90° counterclockwise about the origin takes (2, 0) to (0, 2).
  • glide reflection A reflection paired with a move along the mirror. Reflecting a figure over the x-axis and then sliding it 4 units right is a glide reflection.
  • half-turn A rotation of 180 degrees, one straight angle. A half-turn about the origin takes (3, 2) to (−3, −2).
  • origin The place on a grid where both coordinates are zero. The center of a rotation on a grid is often the origin.
  • prime The small mark written after a letter, as in A'. The image of point A is often named A′, read as A prime.
  • quarter-turn A rotation of 90 degrees, one right angle. Four quarter-turns make one full turn of 360°.
  • vector An arrow that shows a distance and a direction. The vector (3, 2) describes a translation of 3 units right and 2 units up.
  • vertex A tip of a figure, where its edges come together. A triangle has 3 vertices, often named A, B and C.
  • x-axis The horizontal number line of a coordinate grid. A reflection over the x-axis changes the sign of the second coordinate: (4, 1) goes to (4, −1).
  • y-axis The vertical number line of a coordinate grid. A reflection over the y-axis changes the sign of the first coordinate: (4, 1) goes to (−4, 1).

How this list was compiled: Term list chosen for this site on 2026-10-09. Each meaning is written in our own words and was checked that day against the English Wikipedia article on the term (https://en.wikipedia.org/), whose text is under the Creative Commons Attribution-ShareAlike license: Geometric transformation, Translation (geometry), Reflection (mathematics), Rotation (mathematics), 2D rotation (center and angle of rotation), Scaling (geometry) and Dilation (metric space) (dilation, scale factor, enlargement, reduction), Image (mathematics) (image, pre-image), Rigid transformation, Reflection symmetry and Symmetry (geometry) (symmetry, line of symmetry), Rotational symmetry, Point reflection (point symmetry, half-turn), Congruence (geometry), Similarity (geometry), Corresponding sides and corresponding angles, Tessellation, Turn (angle) (quarter-turn, half-turn), Prime (symbol), Glide reflection and Euclidean vector. Each was checked a second time against the entry for the term in Wiktionary, the free dictionary (https://en.wiktionary.org/), under the same license, or, where Wiktionary has no entry or no geometry sense (dilation, line of symmetry, scale factor, enlargement, reduction, corresponding, line of reflection, center of rotation, angle of rotation, rigid transformation, point symmetry, quarter-turn), against the Cambridge Dictionary (https://dictionary.cambridge.org/us/) or a second article of the list above. Every coordinate in the examples was worked out and then checked a second time. The example after each meaning is our own. Licence: own work

How it works

This transformation vocabulary worksheet prints twelve terms down the left and their meanings, mixed up, down the right. It opens on the four transformations. Two more sets cover symmetry and similarity, and the words that describe a move.

Read the full guide

A transformations vocabulary worksheet for the four moves

Set opens on The four transformations: translation, reflection, rotation and dilation, then image, pre-image, rigid transformation, line of reflection, center of rotation, angle of rotation and scale factor. In the list under the tool the first three also carry their everyday names: slide, flip and turn.

Symmetry, similarity and direction

Symmetry and similarity prints symmetry, line of symmetry, rotational symmetry, point symmetry, asymmetric, congruent, similar, corresponding, fixed point, enlargement, reduction and tessellation. Describing the move has x-axis, y-axis, origin, vertex, vector, clockwise, counterclockwise, quarter-turn, half-turn, prime, composition and glide reflection.

  • No grid is printed: the sheet is words and meanings, and the worked coordinates are in the list under the tool.

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 makes it larger or smaller without changing its shape.

What is the difference between an image and a pre-image?

The pre-image is the figure before the transformation and the image is the figure after it. If triangle ABC is reflected onto triangle A′B′C′, then ABC is the pre-image and A′B′C′ is the image.

Which transformations are rigid?

Translations, reflections and rotations: each keeps every distance, so the image is congruent to the pre-image. A dilation by a scale factor of 2 is not rigid. It doubles every length, so the image is similar to the pre-image but not congruent.

What vocabulary about transformations is on the worksheet?

Thirty-six terms in three sets of twelve: the four transformations with image and pre-image, the words for symmetry and similarity, and the words that describe a move, such as clockwise, vector and origin. One set fills one page.

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