Geometric Transformations Flashcards

Grade 10 · Math · Flashcards

Coordinate rules, properties, and vocabulary for all four geometric transformations.

Flashcards

Translation (a, b): (x, y) → (x+a, y+b); a rigid motion, preserves orientation.
Reflection over x-axis: (x, y) → (x, −y); flips orientation.
Reflection over y-axis: (x, y) → (−x, y); flips orientation.
Reflection over y = x: (x, y) → (y, x).
Reflection over y = −x: (x, y) → (−y, −x).
Rotation 90° CCW (origin): (x, y) → (−y, x).
Rotation 180° (origin): (x, y) → (−x, −y).
Rotation 270° CCW (90° CW, origin): (x, y) → (y, −x).
Dilation from Origin, factor k: (x, y) → (kx, ky); lengths ×k, area ×k², angles preserved.
Rigid Motion (Isometry): Preserves distances and angles: translations, reflections, rotations only.
Non-rigid Transformation: Dilation (k ≠ 1) changes lengths but preserves angles → similar, not congruent.
Two Reflections over Intersecting Lines: Equivalent to a rotation by twice the angle between the lines.
Two Reflections over Parallel Lines: Equivalent to a translation of twice the distance between the lines.
Glide Reflection: A translation followed by a reflection over a line parallel to the translation vector; an isometry.