Download transformations cheat sheet and more Quizzes Mathematics in PDF only on Docsity! TRANSFORMATIONS CHEAT-SHEET! REFLECTIONS: Vv Reflections area flip. v The flip is performed over the “line of reflection.” Lines of symmetry are examples of lines of reflection. v Reflections are isometric, but do not preserve orientation. Coordinate plane rules: Over the x-axis: (x, y) > (x, -y) Over the y-axis: (x, y) > (-x, y) Over the line y = x: (x, y) > (y, x) Through the origin: (x, y) > (-x, -y) TRANSLATIONS: Y Translations are a slide or shift. v Translations can be achieved by performing two composite reflections over parallel lines. v Translations are isometric, and preserve orientation. Coordinate plane rules: (x, y) > (x +h, y tk) where h and k are the horizontal and vertical shifts. Note: If movement is left, then h is negative. If movement is down, then k is negative. DILATIONS: v Dilations are an enlargement / shrinking. Y Dilations multiply the distance from the point of projection (point of dilation) by the scale factor. v Dilations are not isometric, and preserve orientation only if the scale factor is positive. Coordinate plane rules: From the origin dilated by a factor of “c”: (x, y) > (cx, cy) From non-origin by factor of “c’: count slope from point to projection point, multiply by “c,” count from projection point. ROTATIONS: ¥ Rotations area turn. Vv Rotations can be achieved by performing two composite reflections over intersecting lines. The resulting rotation will be double the amount of the angle formed by the intersecting lines. v Rotations are isometric, and do not preserve orientation unless the rotation is 360° or exhibit rotational symmetry back onto itself. Vv Rotations of 180° are equivalent to a reflection through the origin. Coordinate plane rules: Counter-clockwise: Clockwise: Rule: 90° 270° (% y) D(-y, x) 180° 180° (x, y) D (-%, -y) 270° 90° (4 y) Py, -X)
