Wiskunde: Rotations and Oriented Angles

Vocabulary flashcards covering oriented angles, rotations, geometric constructions, and coordinate plane rotation rules based on the mathematics lecture notes.

Oriented Angle (Georiënteerde hoek)

An angle that is determined by both an angle magnitude (size) and a direction of rotation.

Clockwise Direction (Wijzerzin)

The direction of rotation established by convention as the negative direction.

Counterclockwise Direction (Tegenwijzerzin)

The direction of rotation established by convention as the positive direction.

Rotation (Rotatie)

A geometric transformation determined by a center $O$ and an oriented angle, where the image of point $A$ is typically denoted $A'$ and preserves distance such that $|OA| = |A'O|$.

Rotation Notation: $R_{(O, \alpha)}(A) = A'$

Notation read as: the rotation of point $A$ around center $O$ over an oriented angle $\alpha$ produces the rotation image point $A'$.

Method for Rotating a Point / Figure

A three-step construction procedure: 1. Draw ray $[OA$. 2. Draw the angle with $[OA$ as the initial side (e.g., $70^\circ$). 3. Use a compass to construct image point $A'$ on the terminal side such that $|OA| = |A'O|$.

Point Reflection (Puntspiegeling)

A rotation with center $O$ over an oriented angle of $180^\circ$ or $-180^\circ$.

Coordinate Rule: $180^\circ$ Rotation Around the Origin

If point $A(x, y)$ undergoes rotation $R_{(O, 180^\circ)}(A) = A'$, the coordinates become $A'(-x, -y)$ (e.g., $P(-3, 2) \rightarrow P'(3, -2)$).

Coordinate Rule: $90^\circ$ Rotation Around the Origin

If point $A(x, y)$ undergoes rotation $R_{(O, 90^\circ)}(A) = A'$, the coordinates become $A'(-y, x)$ (e.g., $Q(1, 2) \rightarrow Q'(-2, 1)$).

Coordinate Rule: $-90^\circ$ Rotation Around the Origin

If point $A(x, y)$ undergoes rotation $R_{(O, -90^\circ)}(A) = A'$, the coordinates become $A'(y, -x)$ (e.g., $R(1, -3) \rightarrow R'(-3, -1)$).