Intermediate Algebra
Coordinate Transformations
Move shapes on the coordinate plane: slide, turn, flip, scale and stretch them, write each move in coordinates, and use moves to tell when two shapes are congruent or similar.
THE SYLLABUS
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Translating Points
A translation by (a, b) shifts every point a steps right and b steps up, and any number of points travel together.
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Negative Translations
In a translation by (a, b), a positive a goes right and a negative a goes left; a positive b goes up and a negative b goes down.
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Translating Shapes
A translation acts on every vertex of a shape, so the whole shape travels; the translation found for one vertex works for the whole shape.
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Combining Translations
A translation by (a, b) followed by one by (c, d) does the same as one translation by (a + c, b + d); any number of translations in a row equal a single one.
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Undoing Translations
A translation by (a, b) is undone by the translation by (−a, −b), its inverse; any chain of translations is undone by one translation.
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Level Check
Ten questions from Level 1: translations to targets, single translations equal to chains of them, and translations that undo others.
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