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Geometry
Transformations - Translations
A translation (slide) moves every point of a figure the same distance in the same direction. Properties of translations: • Shape and size are preserved (congruent) • Orientation stays the same • Parallel lines remain parallel Notation: • (x, y) → (x + a, y + b) • Move right: add to x • Move left: subtract from x • Move up: add to y • Move down: subtract from y
Example:
Translate triangle ABC with vertices A(1,2), B(3,5), C(4,1) by moving 3 units right and 2 units down. Rule: (x, y) → (x + 3, y - 2) A(1,2) → A'(1+3, 2-2) = A'(4,0) B(3,5) → B'(3+3, 5-2) = B'(6,3) C(4,1) → C'(4+3, 1-2) = C'(7,-1)