Translations, Reflections, and Rotations
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1 * Translations, Reflections, and Rotations
2 Vocabulary Transformation- changes the position or orientation of a figure. Image- the resulting figure after a transformation. Preimage- the original figure. Translation- figure slides along a straight line without turning. Reflection- figure flips across a line of reflection, creating a mirror image. Line of reflection- the line in which a figure flips across to create a mirror image. Rotation- figure turns around a fixed point.
3 In mathematics, a transformation changes the position or orientation of a figure. The resulting figure is the image of the original figure, called the preimage. Images resulting from the transformations described in the next slides are congruent to the original figures.
4 Types of Transformations Translation The figure slides along a straight line without turning.
5 Types of Transformations Reflection The figure flips across a line of reflection, creating a mirror image.
6 Types of Transformations Rotation The figure turns around a fixed point.
7 Additional Example 1: Identifying Types of Transformations Identify each type of transformation. A. B. The figure flips across the y-axis. It is a reflection. The figure slides along a straight line. It is a translation.
8 Check It Out: Example 1 Identify the type of transformation.
9 Additional Example 2: Graphing Transformations on a Coordinate Plane Graph the translation of quadrilateral ABCD 4 units left and 2 units down. Each vertex is moved 4 units left and 2 units down.
10 Additional Example 2 Continued Write the coordinate of the vertices of the image. Quadrilateral ABCD (x 4, y 2) A B C D A(1, 3) (1 4, 3 2) A ( 3, 1) B(4, 4) (4 4, 4 2) B (0, 2) C(4, 1) (4 4, 1 2) C (0, 1) D(1, 1) (1 4, 1 2) D ( 3, 3) The coordinates of the vertices of quadrilateral A'B'C'D' are A'( 3, 1), B'(0, 2), C'(0, 1), and D'( 3, 3).
11 Reading Math A is read A prime and is used to represent the point on the image that corresponds to point A of the original figure
12 Check It Out: Example 2 Graph the translation of quadrilateral ABCD 5 units left and 3 units down.
13 Additional Example 3: Graphing Reflections on a Coordinate Plane Graph the reflection of the figure across the indicated axis. Write the coordinates of the vertices of the image.
14 Additional Example 3 Continued A. x-axis The x-coordinates of the corresponding vertices are the same, and the y-coordinates of the corresponding vertices are opposites. The coordinates of the vertices of triangle A D C are A ( 3, 1), D (0, 0), and C (2, 2).
15 Additional Example 3 Continued B. y-axis The y-coordinates of the corresponding vertices are the same, and the x-coordinates of the corresponding vertices are opposites. The coordinates of the vertices of triangle A D C are A (3, 1), D (0, 0), and C ( 2, 2).
16 Check It Out: Example 3 Graph the reflection of quadrilateral ABCD across the x-axis.
17 Additional Example 4: Graphing Rotations on a Coordinate Plane Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0). Rotate ABC 180 about the origin. Write the coordinates of the vertices of the image. C 3 3 B y A A B C x The corresponding sides, AC and AC make a 180 angle. Notice that vertex C is 4 units to the right of vertex A, and vertex C is 4 units to the left of vertex A. The coordinates of the vertices of triangle A B C are A (0, 0), B ( 2, 3), and C ( 4, 0).
18 Check It Out: Example 4 Rotate the graph of quadrilateral ABCD 90 clockwise about the origin.
R(-14, 4) R'(-10, -2) S(-10, 7) S'(-6, 1) T(-5, 4) T'(-1, -2)
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