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MATH 01310 · College Geometry

MATH 01310 · Transformations & coordinate geometry

Isometries vs dilations

Definition

Isometries (translations, rotations, reflections — and glide reflections) preserve distance and congruence. Dilations scale distances from a center by factor k and create similarity (not generally congruence unless |k|=1).

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Composition of isometries is an isometry. Reflections generate the others.

Coordinate rules: reflect over axes, rotate 90° about origin, translate by vector.

Dilations: (x,y)→(kx,ky) about origin; more generally about a center C.

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  1. 1.Describe a sequence of isometries mapping one congruent triangle onto another.