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Advanced Geometry Rigid Transformations Lesson 2 Reflections Reflection flip Line of Reflection http://www.mathsisfun.com/flash.php?path=%2Fgeometry/images/reflecti on.swf&w=670.5&h=579&col=%23FFFFFF&title=Geometry+-+Reflection Pre-image Image N E N A T E P T A P Example: Draw the reflected image of quadrilateral WXYZ in line p. Example: Name the image of each figure under a reflection in line l . F BC D BA trapezoid FHGA Example: Quadrilateral ABCD has vertices A(1, 1), B(3, 2), C(4, -1), and D(2, -3). Graph ABCD and its image under reflection in the x-axis. Example: Triangle RST has vertices R( -1, 3), S(-5, -2), and T(2, 4). Graph RST and its image under reflection in the y-axis. Example: Quadrilateral RUDV has vertices R(-2, 2), U(3, 1), D(4, -1), and V(-2, -2) and is reflected in the origin. Graph RUDV and its image. To reflect in the origin, reflect over both the x-axis AND y-axis. Example: Triangle XYZ has vertices X(4, -2), Y(2, -3), and Z(3, -5). Graph XYZ and it image under reflection in the line y = x. Example: Rectangle JKLM has vertices J(0, 2), K(0, -2), L(3, 2), and M(3, -2). Graph JKLM and its image under reflection in the line y = -x. If a figure can be folded so that the two halves match exactly, the fold is called a line of symmetry. For some figures, a common point of symmetry, called a point of reflection, exists for all points on a figure Example: Determine how many lines of symmetry the figure has and draw them. Then determine whether the figure has point symmetry. A point of symmetry is the midpoint of all line segments joining opposite points of the figure.