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Advanced Geometry Rigid Transformations Lesson 2

This lesson focuses on the concept of reflection in advanced geometry, particularly rigid transformations. Through illustrative examples, students will learn how to draw the reflected images of various geometrical figures, including quadrilaterals and triangles, across different lines, such as the x-axis and y-axis, as well as the origin. Additionally, the lesson covers important concepts such as lines of symmetry and points of reflection, helping students grasp the visual and mathematical aspects of reflection in geometry.

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Advanced Geometry Rigid Transformations Lesson 2

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  1. Reflections Advanced Geometry Rigid Transformations Lesson 2

  2. Reflection flip Line of Reflection http://www.mathsisfun.com/flash.php?path=%2Fgeometry/images/reflection.swf&w=670.5&h=579&col=%23FFFFFF&title=Geometry+-+Reflection

  3. Pre-image Image N E E  N P P T A A T

  4. Example: Draw the reflected image of quadrilateral WXYZ in line p.

  5. Example: Name the image of each figure under a reflection in line F D trapezoid FHGA

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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

  12. 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.

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