Transformations Summary

Geometry · Axiom Academy

SUMMARY Unit 8 Summary: Transformations Moving shapes around the plane — sliding, flipping, turning, and resizing — and writing each motion as a clean rule on coordinates. A transformation maps every point of a figure to a new location. Translations, reflections, and rotations are rigid motions (isometries) — they preserve distance and angle, so the image is congruent to the original. Dilation is the odd one out: it scales by a factor k from a center, so it changes size — the image is similar , not congruent (unless |k| = 1 ). Every rigid motion has a tidy coordinate rule . Reflect over the x -axis negates y ; over the y -axis negates x ; over y = x swaps the two. A composition applies one transformation then another. Order matters in general — doing A then B usually differs from B then A . A figure has line symmetry if a reflection maps it onto itself, and rotational symmetry if a rotation under does. Core Concept Translations (Slides) A translation slides every point the same distance in the same direction — described by a vector . It's a rigid motion : shape, size, and orientation are all unchanged. When to use: moving a figure without turning or flipping it. Watch out for: a and b can be negative — that's a slide left/down. Core Concept Reflections (Flips) A reflection flips a figure across a line of reflection, producing a mirror image. It's rigid , but it reverses orientation (a left hand becomes a right hand). When to use: creating mirror images; building symmetry.

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