* Translations, Reflections, and Rotations
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.
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.
Types of Transformations Translation The figure slides along a straight line without turning.
Types of Transformations Reflection The figure flips across a line of reflection, creating a mirror image.
Types of Transformations Rotation The figure turns around a fixed point.
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.
Check It Out: Example 1 Identify the type of transformation.
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.
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).
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
Check It Out: Example 2 Graph the translation of quadrilateral ABCD 5 units left and 3 units down.
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.
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).
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).
Check It Out: Example 3 Graph the reflection of quadrilateral ABCD across the x-axis.
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).
Check It Out: Example 4 Rotate the graph of quadrilateral ABCD 90 clockwise about the origin.