 # Perform Congruence Transformations. A __________________ is an operation that moves or changes a geometric figure to produce a new figure called an __________.

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Perform Congruence Transformations

A __________________ is an operation that moves or changes a geometric figure to produce a new figure called an __________. transformation image

3 Main Types of Transformations ______________________ – moves every point in the figure the same distance in the same direction ______________________ – uses a line of reflection to create a mirror image ______________________ – turns a figure about a fixed point, called the center of rotation Translation Reflection Rotation

Example 1 Name the type of transformation demonstrated in each picture. a.b.c. Reflection in a horizontal line Rotation about a point Translation in a straight path

Example 2 Translate a figure in the coordinate plane. Quadrilateral ABCD has vertices A(-6,2), B(-6,6), C(-4,6), and D(-2,2). Sketch the quadrilateral and its image after translation (x,y)  (x + 5, y – 2) A’(–1, 0)B’(–1, 4) C’(1, 4)D’(3, 0) B AD C C’B’ A’D’

Example 3 Describe the translation of the figure below (x, y)  (____, ____). x – 3 y – 5

(–3, 2) (–5, 7) (–5, 2) (–3, –2) (–5, –7) (–5, –2) x–y

Example 5 Give the (x, y) coordinates for the triangle. Then reflect the image over the y-axis. Give the (x, y) coordinates for the image. (x, y)  (x, y) image Therefore, when you reflect over the y-axis, (x, y)  (____, ____) (–3, 2) (–5, 7) (–5, 2) (3, 2) (5, 7) (5, 2) –xy

Example 6 Reflect over the x-axis. Example 7 Reflect over the y-axis.

EF D A B C Translate one unit to the right and one unit down (x + 1, y – 1)

Example 9- Rotation(about the origin) Rotate the figure 90° clockwise.

Example 10 Rotate the figure 270° counterclockwise.

Homework: Transformations Packet page 14

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