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

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