Definition
Translation by vector u: M → M' such that MM' = u. Preserves distances and angles.
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Lesson overview
This lesson brings together the PDF, study notes and chapter flow so you can revise Plane Transformations without losing the thread.
Definition
Translation by vector u: M → M' such that MM' = u. Preserves distances and angles.
Image of a line
The image of a line under a translation is a parallel line.
Axial symmetry (about a line D)
M' is the reflection of M about D if D is the perpendicular bisector of MM'. Preserves distances.
Central symmetry (about O)
M' is the image of M about O if O is the midpoint of MM'.
Rotation of center O and angle θ
Rotates each point M by angle θ around O. Preserves distances.
Homothety of center O, ratio k
OM' = k·OM. Preserves angles. Distances are multiplied by |k|.
Problem-solving method
Identify data, set formulas, solve step by step, then verify sign, unit, and coherence.
Common mistakes
Forgetting domain constraints, mixing equality/equivalence, and losing solutions during transformations.