1. An operation that moves or changes a geometric figure (a preimage) in some way to produce a new figure (an image). Congruence transformations – Changes the position of the figure without changing the size or shape Translation Reflection Rotation 4.8 Transformations

2. The vertices of ABC are A(4, 4), B(6, 6), and C(7, 4). The notation (x, y) → (x + 1, y – 3) describes the translation of ABC to DEF. What are the vertices of DEF? A Translation: moves every point of a figure the same distance and in the same direction Coordinate notation: (x,y) (x+a,y+b)

3. Uses a line of reflection to create a mirror image of the original figure. Coordinate notation for reflection in the x-axis : (x,y) (x, -y) Coordinate notation for reflection in the y- axis: (x, y) (-x, y) A Reflection

4. Reflect a figure in the x-axis Reflection

5. Turns a figure about a fixed point called the center of rotation Direction: Clockwise or counterclockwise Center of rotation: The origin Angle: (90˚,180˚,270˚) Angles of rotation formed by rays drawn from the center of rotation through corresponding points on the pre-image and image Rotation

6. Graph AB and CD. Tell whether CD is a rotation of AB about the origin. If so, give the angle and direction of rotation. A(–3, 1), B(–1, 3), C(1, 3), D(3, 1) Rotation

7. Tell whether PQR is a rotation of STR. If so, give the angle and direction of rotation. Rotations

8. Name the type of transformation demonstrated in each picture. a. b. c. Which Transformation?

9. A transformation that stretches or shrinks a figure to create a similar figure. A figure is reduced or enlarged with respect to a fixed point called the center of dilation. 6.7 Dilations

10. The scale factor of a dilation is the ratio of the side length of the image to the corresponding side length of the original figure Coordinate notation for a dilation with respect to the origin: (x,y) ( kx, ky) Reduction: 0 < k < 1 Enlargement : k > 1 Dilations

11. Draw a dilation of quadrilateral ABCD with vertices A(2, 1), B(4, 1), C(4, – 1), and D(1, – 1). Use a scale factor of 2. Dilations