1. Properties or Rules of Transformations Equations used to find new locations

2. Translation What do you Notice about this Translation going From blue to red? How are the Ordered pairs Affected?

3. Translation Basic Translation (x,y)  (x+3,y) Move each point 3 units right on the x axis Could rules for x, y or both Add to the x moves right Subtract from x moves left Add to y moves up Subtract from y moves down

4. Reflection 3 types Over the x axis Over the y axis Over the line y=x

5. Example Given the following picture reflect over the y axis and the write the coordinates

6. Reflections What do you think will happen with the x axis reflection? (x,y)  (x,-y) Reflecting about the line y=x? (x,y)  (y,x)

7. This is reflection along the line y=x, notice the location of the original points and how they are different in the new image, x and y are reversed Point (-1,2) Point (-4,1) Point (-3,5) Point (2,-1) Point (1,-4) Point (5,-3)

8. Rotation about Origin Rotate a figure 180 degrees about the origin what do you notice Rotate a figure 90 degrees clockwise or counter clockwise what do you notice?

9. OldNew XYX’Y’ 23-2-3 51-5 46-4-6 Rule (x,y)  (-x,-y)

10. OldNew XYX’Y’ 233-2 511-5 466-4 Rule (x,y)  (y,-x)

11. Coordinate Transformation Reflect across y-axis the rule (x,y)  (-x,y) Reflect across x-axis the rule (x,y)  (x,-y) Reflect across y=x the rule (x,y)  (y,x) Rotate about the origin 180 degrees the rule (x,y)  (-x,-y) Translation about x-axis (x,y)  (x+ or - #,y) Translation about y-axis (x,y)  (x,y+ or - #)

12. Homework Pg 380 1-8