1. Transformations Translation Reflection Rotation Dilation

2. Transformation Changing the position (location) or size of a figure We will be focusing on 2 Dimensional figures on the coordinate plane

3. Translation Moving a figure around the coordinate system Sliding it left, right, up or down, all the points (vertices) are moved the same

4. Problem 3.1

5. Problem 3.1 B,C and D When you translate a figure all the parts are congruent, meaning the same as the original

6. Reflection A transformation that flips an image over a line called the line of reflection Think of a mirror image on the other side of a line The image has things backwards We are only going to do reflection over the x and y axis

7. Problem 3.2 A.When reflecting an image over a line the original image and the new image are the same distance from the line of reflection B.The lines are opposite, the original is negative the reflection is positive C.The images would be exactly on top of each other Distances are the same to the line of reflection Triangles are still congruent or the exact same

8. Rotation Turns a figure around a fixed point, in this case the origin We are also only going to talk about rotations that are 90,180, or 270 degrees, but we may refer to a specific direction Center of Rotation – origin or fixed point you are turning the figure around Clockwise and Counterclockwise direction

9. Problem 3.3 Try to do the rotation and see if as a group you can come up with an explanation of how to do this

10. Problem 3.4 Vertex is not the center of rotation, it can be but isn’t always

11. Rules/Ideas for Transformations Translate – moving each on the vertices the same L,R, up or down, could be one or two things for each point, figures are congruent Reflection – mirror image over the x or y axis, find the distance the original vertex is from the line of reflection and move the same distance to the other side, do with all points and connect Rotation – Write down the coordinates of the original figure, turn the paper until the quadrant the new figure will appear in is in the upper left (where quadrant 1 originally was) re-plot the points

12. Rules/Equations If it is easier to apply an equation to each of the rules Translation – (x,y)  (x+ #,y) right (x,y)  (x-#,y) left (x,y)  (x,y+#) up (x,y)  (x,y-#) Down

13. More Reflection over y-axis (x,y)  (-x,y) Reflection over x-axis (x,y)  (x,-y) Rotation 180 about origin (doesn’t matter direction) (x,y)  (-x,-y) Rotation 90 clockwise about origin (x,y)  (y,-x) Rotation 90 counterclockwise (x,y)  (-y,x)

14. Homework Page 18 2,3,5,9 Worksheets for translation, reflection, rotation