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