1. Translations, Reflections, & Glide Reflections
October 21st, 2013

2. Vocabulary Transformation-change in position, shape, or size
Preimage-original figure
Image-resulting figure (indicate with a ’ after the letter)
Isometry- when the preimage and image are congruent

3. Graph Paper Draw Triangle DEF (with endpoints on grid lines)
Write in the coordinates.
Add 3 to the x coordinates
Add 5 to the y coordinates
Plot these three points.
Label them as D’E’F’

4. What happened? Change in Size? Change in Shape? Change in Position?
Where did it go?

5. Translation
Moves all points the same distance in the same direction (Slide)
This is an ISOMETRY
We use a TRANSLATION RULE
to indicate where the image is.
How did triangle ABC move?
5 left and 2 up
We write the translation rule as:
(x, y)→(x – 5, y + 2)

6. Write the Translation Rule
Translate 3 to the right and 5 up.
(x, y)→(x+3, y+5)
3 left and 5 down
(x, y)→(x-3, y-5)

7. Translation Here is WXYZ and W’X’Y’Z What is the Translation Rule?
(x, y)→(x+5, y-1)

8. Reflection A flip across line r called the LINE OF REFLECTION where:
If A is on r, then A=A’
If B is not on r, then r bisects BB’
This is an ISOMETRY

9. Reflection Plot Triangle H(2, 4), I (-3, 1), J(4, -2) on 3 graphs
Plot H’I’J’ reflected over the x-axis
Plot H’I’J’ reflected over the y-axis
Plot H’I’J’ reflected over the line y = x
What happens with the coordinates?
Reflect over x-axis: change y-coordinate’s sign
Reflect y-axis: change x-coordinate’s sign
Reflect over the line y = x: switch the coordinates

10. Plot Triangle H(2, 4), I (-3, 1), J(4, -2)

11. Reflect over the line… What does the line y = 3 look like?
What does the line x = -2 look like?

12. On a graph Use Translation Rule: (x, y)→(x – 4, y+2)
Plot triangle RST; R(2, 2) S(-1, 3) T(0, 4)
Use Translation Rule: (x, y)→(x – 4, y+2)
Label the result of a translation R’S’T’
Reflect R’S’T’ over the y-axis
Label this image R’’S’’T’’
What are the coordinates of R”S”T”?

13. What did you just do?
How would you describe the transformation you just did?
Think about from RST→R”S”T”
Composition of Transformations- do the second transformation on the image of the first

14. Glide Reflection GLIDE(translation) followed by a REFLECTION
This is also an ISOMETRY

15. Try Some Graph the image of the Glide Reflection:
(x, y) → (x, y + 1); x = 2

16. Try Some Graph the image of the Glide Reflection:
(x, y) → (x + 3, y + 3); y = x

17. Homework
Worksheet

18. Warm Up What is the translation rule?
What is the image after reflecting (2, 3) over the line y = 2x + 1?
Identify the transformation of
ABCD to OPQR.

19. Rotations

20. Rotations ROTATE x˚ about point Z. X = angle of rotation
Z = Center of rotation
This is an ISOMETRY

21. Rotations
When you rotate an object (point), it will stay the SAME distance from the center of rotation.

22. Rotations We will ALWAYS rotate about the origin
On a graph:
We will ALWAYS rotate about the origin
We will only rotate 90˚ or 180˚

23. Use what we know… What do you know about 180˚?
Straight line, straight angle
So we will draw a line connecting the ORIGIN and our PREIMAGE point. (Extend past the origin.)
Measure the distance from the ORIGIN to your PREIMAGE.
Use this measurement to find the image point.
The point equidistant from the origin is the IMAGE.

24. Rotate 180˚ You need to rotate each point individually
Connect the original point to the origin and extend
Measure the distance (preimage to origin)
Measure the extension (origin to equidistant)
Mark your image point
What are the coordinates of S’U’N’?
What do you notice about the coordinates?

25. 90˚ rotations
After you draw a line through the origin, use your PROTRACTOR to draw another line at 90˚
Notice the direction: clockwise or counterclockwise
Measure the distance from the origin to the preimage
Measure along the perpendicular line. The same distance from above will locate your image.

26. Rotate 90˚ You need to rotate each point individually
Connect the original point to the origin and extend
Draw in the perpendicular line
Measure the distance (preimage to origin)
Measure the perp. line (origin to equidistant)
Mark your image point
What are the coordinates of A’B’C’D’?
What do you notice about the coordinates?

27. Rotations 180˚ rotation: negate each coordinate 90˚ clockwise:
switch coordinates, negate new y-coordinate
90˚ counterclockwise:
switch coordinates, negate new x-coordinate

28. Regular Polygons
Regular: all sides are congruent and all angles are congruent
360˚ around center
Degree measure of each angle around the center?
360 ÷ (# of sides)
72˚

29. Regular Polygons Rotate P: 144˚ to the right
Rotate T: 216˚ to the right
Rotate PE: 72˚ to the right P E A T N

30. Homework
Worksheet