1. Warm-Up
2. What type of symmetry does the figure to the right have? How do you know?

2. Pre-image
The original figure before undergoing a transformation.

3. Image
The new, resulting figure after a transformation

4. Isometry
A transformation in which the preimage and image are congruent.

5. Which of the following are isometric?

6. they preserve angle measures
Isometries not only
preserve lengths, but
they preserve angle measures
parallel lines, and
betweenness of points

7. Parallelogram MATH is transformed to Parallelogram LOVE by a rotation
Parallelogram MATH is transformed to Parallelogram LOVE by a rotation. What is the image of HT? M A E V L H T EV O

8. Find the value of each variable, given that the transformation is an isometry.

9. * Translations
(Slide your image over)
* image
* preimage

10. * Reflections
(Flip your image over)
* preimage
* image

11. * Rotations
(Turn your image
about a fixed point)
* image
* preimage

12. (Enlarge or Shrink your image)
* Dilations
(Enlarge or Shrink your image)
* preimage
* image

13. Translations

14. Every point of the shape must move:
To translate a shape:
Every point of the shape must move:
The same distance
In the same direction

15. Translations
Adding/ subtracting to the x and y variables generates a TRANSLATION on the coordinate plane.
Adding to the X variable moves the pre-image RIGHT (x + 3, y)
Subtracting from the X variable moves the pre-image LEFT . (x-3, y)
Adding to the Y variable moves the pre-image UP. (x, y+2)
Subtracting from the Y variable moves the pre-image DOWN. (x, y-2)

16. Example 1: Identify what the rule does to the pre-image.
( x + 1, y - 1) =
(x -1, y + 1) =

17. Example 2: Identify the rule for a translation of the figure below 6 units right and 3 units down.

18. Example 3: Translate the image ABC by (x – 8, y + 2), given that ABC has the coordinates A(-2, 4), B (0, -8) and C (-3,5)

19. Practice!

20. Dilations

21. Dilations
A Dilation is the ENLARGING or SHRINKING of a shape.

22. Dilation Notation
Dk (x, y) = (kx, ky)

23. Example 1:
Dilate the figure ABC by (2x, 2y) given that A (-2,-2) B(1,-1) and C(0, 2). What are the new coordinates?

24. Independent Practice

25. Exit Ticket
Given figure ABC with coordinates A(1,4) B(2, 6) and C(-3, 2)
Translate the figure using the rule T3,-2 (x+3, y – 2)
Dilate the figure using the rule D1/3 or (1/3x, 1/3y)