Translation, Dilation & Tessellations

30 vocabulary-style flashcards covering key terms and definitions on translation, dilation, tessellations, and related geometric transformations.

Translation

A rigid (isometric) transformation that slides every point of a figure the same distance in a given direction without rotating, reflecting, or resizing the shape.

Translation Vector

An ordered pair (h,k) that indicates the horizontal and vertical distances a figure moves during a translation.

Rigid Transformation (Isometry)

A transformation that preserves size and shape; the pre-image and image are congruent (e.g., translations, rotations, reflections).

Sliding Movement

The characteristic motion of a translation in which all points travel along parallel paths for equal distances.

Fixed Point (under Translation)

A point that remains unmoved by a transformation; translations have none unless the vector is zero.

Dilation

A transformation that enlarges or reduces a figure relative to a fixed point (center of dilation) by a scale factor k, preserving shape but not size.

Center of Dilation

The fixed point from which all points of a figure move outward or inward during dilation.

Scale Factor (k)

The ratio that determines the magnitude of a dilation: k>1 enlarges, 0<k<1 reduces, k=1 leaves size unchanged.

Non-Rigid Transformation

A transformation that changes a figure’s size or shape; dilations are non-rigid because they alter size.

Similarity (Under Dilation)

Relationship between the pre-image and image of a dilation; corresponding angles are equal and corresponding sides are proportional.

Area Scaling Factor

For a dilation with scale factor k, the area of the image equals k² times the area of the pre-image.

Volume Scaling Factor

For 3-D figures, a dilation with scale factor k multiplies volume by k³.

Tessellation (Tiling)

A repeating pattern of one or more shapes that completely covers a plane without gaps or overlaps.

Tile

An individual shape used repeatedly to form a tessellation.

Vertex Condition

Rule stating that the angle measures of tiles meeting at any vertex of a tessellation must sum to exactly 360°.

Regular Tessellation

A tessellation formed by only one type of regular polygon; possible with equilateral triangles, squares, or regular hexagons.

Semi-Regular Tessellation

A tessellation made from two or more kinds of regular polygons arranged identically at every vertex; eight such patterns exist.

Irregular Tessellation

A tessellation composed of irregular polygons or a mixture of regular and irregular polygons.

Escher-Type Tessellation

An artistic tessellation created by altering the sides of a basic tiling polygon so the tiles become recognizable figures (e.g., birds, fish) that interlock perfectly.

Translation Symmetry

Property of a pattern that can be shifted (translated) along a vector and still coincide with itself.

Rotation (in Tessellations)

A rigid transformation turning a tile around a point by an angle (often a divisor of 360°) to help the pieces fit together in a tessellation.

Reflection (in Tessellations)

A flip of a tile across a line, producing a mirror image that can adjoin the original in a tessellation.

Glide Reflection

A composite transformation consisting of a translation followed by a reflection across a line parallel to the direction of translation; often yields “walking” patterns.

Frieze Pattern

A design that repeats infinitely in one direction along a strip, created through combinations of translations, reflections, rotations, and glide reflections.

Enlargement

A dilation with scale factor k>1, producing a larger image similar to the original figure.

Reduction

A dilation with scale factor 0<k<1, producing a smaller image similar to the original figure.

Parallelism Preservation

Property maintained by translations and dilations where parallel lines in the pre-image remain parallel in the image.

Orientation Preservation

Characteristic of translations and non-negative dilations whereby the figure’s facing direction is unchanged (negative k in dilation reverses orientation).

Congruence (Under Isometry)

Exact equality in size and shape between a figure and its image after a rigid transformation.

Similarity Transformation

A mapping (e.g., dilation, or dilation combined with isometries) that produces an image similar to the original figure.