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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 1Name 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 2Translate 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•
A• •D
•C
•C’B’•
A’• •D’
Example 3Describe the translation of the figure
below (x, y) (____ , ____).x – 3 y – 5
Example 4- ReflectionsGive the (x, y) coordinates for the triangle. Then reflect the image over the x-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)
x
–y
Example 5Give 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)
–x y
Example 6 Reflect over the x-axis.
Example 7Reflect over the y-axis.
Example 8The vertices of ABC are A(1, 2), B(0, 0), and C(4,0). A translation of ABC results in the image of DEF with vertices D(2, 1), E(1, -1), and F(5, -1). Describe the translation in words and in coordinate notation.
•• •
•• •E F
DA
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 10Rotate the figure 270° counterclockwise.
Homework: Transformations Packet
page 14