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Geometry 4.8

Geometry 4.8. Perform Congruence Transformations. Transformations : when you move or change a geometric figure in some way to produce a new figure. Image is what the new figure is called.

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Geometry 4.8

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  1. Geometry 4.8 Perform Congruence Transformations

  2. Transformations: when you move or change a geometric figure in some way to produce a new figure. Image is what the new figure is called. Congruence Transformations: changing the position of a figure without changing its size or shape. There are 3 types of transformations. Translation: is when we move every point on the figure, the same distance and direction. Reflection: is when we use a line of reflection to create a mirror image of the original figure. Rotation: Turns a figure about a fixed point called the center of rotation

  3. Coordinate Notation for a translation: (x,y) (x+a, y+b) Which shows that each point (x,y) of the blue figure is translated horizontally a units and vertically b units y x b a

  4. Coordinate Notation for a Reflection : • Reflection in the x-axis • Reflection in the y-axis y y (x,y) (x,y) (-x,y) x x (x,-y) Multiply the y coordinate by -1 (x,y) (x,-y) Multiply the x coordinate by -1 (x,y) (-x,y)

  5. Rotation • 90 clockwise Rotation • 60 counterclockwise rotation y y x x

  6. Example: Name the type of transformation

  7. Example • Figure ABCD has the vertices A(-4, 3), B(-2, 4), C(-1, 1), and D(-3, 1). Sketch ABCD and its image after the translation (x, y)  (x+5, y-2).

  8. Example • Figure WXYZ has the vertices W(-1, 2), X(2, 3), Y(5, 0), and Z(1, -1). Sketch WXYZ and its image after the translation (x, y)  (x-1, y+3).

  9. ExAMPLE • Use coordinate notation to describe the translation. • 5 units right, 3 units up • 7 units left, 4 units down

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