Chapter 2: Transformations and Symmetry (Transformaties en Symmetrie)

Vocabulary practice flashcards covering Chapter 2: Transformations and Symmetry, including reflections, translations, rotations, point reflections, transformation properties, and planar and spatial symmetries.

Spiegeling (Line Reflection)

A transformation of the plane denoted by $s_a$, completely determined by a reflection axis ($\text{spiegelas}$) line $a$.

Spiegelas (Reflection Axis)

The line $a$ that fixes a reflection; any point on this line maps to itself, while any point not on the line forms a segment with its image for which this line is the perpendicular bisector ($\text{middelloodlijn}$).

Origineel en Beeld (Original and Image)

The starting geometric figure ($\Delta ABC$) and its resulting transformed figure ($\Delta A'B'C'$), whose corresponding vertices are always written in the exact same order.

Verschuiving / Translatie (Translation)

A planar transformation completely determined by a directed line segment ($\text{georiënteerd lijnstuk}$), also known as a vector.

Georiënteerd lijnstuk / Vector (Directed Line Segment)

A line segment equipped with an arrow that has a specific direction ($\text{richting}$), length ($\text{lengte}$), and sense ($\text{zin}$), denoted from initial point $A$ to terminal point $A'$ as $AA'$.

Georiënteerde hoek (Directed Angle)

An angle equipped with an arrow that indicates the sense or direction of rotation ($\text{draaizin}$).

Positieve draaizin (Positive Sense of Rotation)

Rotation in the counterclockwise direction ($\text{tegenwijzerzin}$).

Negatieve draaizin (Negative Sense of Rotation)

Rotation in the clockwise direction ($\text{wijzerzin}$).

Draaiing / Rotatie (Rotation)

A transformation determined by a center point ($\text{centrum}$) and an angle of rotation ($\text{draaihoek}$), denoted as $r_{(centrum, hoek)}$, where the center point is mapped onto itself.

Gelijkheid van draaiingen (Equivalence of Rotations)

The property that rotating over an angle of $120^\circ$ in the clockwise sense ($\text{wijzerzin}$) is identical to rotating over an angle of $240^\circ$ in the counterclockwise sense ($\text{tegenwijzerzin}$).

Puntspiegeling (Point Reflection)

A rotation through an angle of $180^\circ$, denoted by $s_O$; its center point maps onto itself, while any other point forms a line segment with its image whose midpoint is the center.

Transformaties van het vlak (Transformations of the Plane)

Geometric mappings—specifically translations, reflections, point reflections, and rotations—characterized by the fact that every point in the plane receives exactly $1$ image in the plane.

Bewaarde eigenschappen van transformaties (Invariants of Transformations)

Five geometric properties preserved by reflections, translations, rotations, and point reflections: collinearity, distance, angle size (including perpendicularity), area, and parallelism.

Collineaire punten (Collinear Points)

Points that lie on the exact same straight line.

Afbeelding van een rechte (Line Mapping under Translation and Point Reflection)

The rule that both a translation ($\text{verschuiving}$) and a point reflection ($\text{puntspiegeling}$) always map a straight line onto a line that is parallel to it.

Lijnsymmetrische figuur (Line-Symmetric Figure)

A plane figure that maps onto itself under a reflection across a line.

Symmetrieas (Axis of Symmetry)

The axis of reflection ($\text{spiegelas}$) across which a line-symmetric figure has itself as its image.

Draaisymmetrische figuur (Rotational Symmetric Figure)

A plane figure that maps onto itself under a rotation.

Puntsymmetrische figuur (Point-Symmetric Figure)

A figure that maps onto itself under a point reflection or a rotation through an angle of $180^\circ$.

Symmetriemiddelpunt (Center of Symmetry)

The center of the point reflection that maps a point-symmetric figure onto itself.

Schuifsymmetrische figuur (Translational Symmetric Figure)

A geometric figure that maps onto itself under a translation ($\text{verschuiving}$).

Vlaksymmetrische ruimtefiguur / Symmetrievlak (Plane-Symmetric Solid / Plane of Symmetry)

A 3D spatial figure, such as a rectangular prism ($\text{balk}$), that has a mirror plane ($\text{symmetrievlak}$) across which it is symmetric.

Puntsymmetrie van een kubus (Point Symmetry of a Cube)

The geometric property of a cube ($\text{kubus}$) being point-symmetric, where its geometric center acts as its center of symmetry ($\text{symmetriemiddelpunt}$).

Bol (Sphere)

The spatial solid with the most symmetry; it has infinitely many planes of symmetry (every plane passing through its midpoint), and its midpoint serves as its center of symmetry ($\text{symmetriemiddelpunt}$).