1. DRILL
If A is in between points B and C and AC is 4x + 12 and AB is x – 4 and BC is 57 feet how long is AB?
Angles A and B are Supplementary if Angle A is 2x – 20 and Angle B is 4x – 44. Find the measure of Angle A.

2. Unit 2 Transformations:
Honors
Geometry

3.                                                                                                                                                                                                                                                                           
Transformations
A transformation is any type of movement in geometry, it can be a change in shape, size, or simply location of an object.
The three types of Transformations we will talk about today are Reflections, Rotations and Translations.

4. Reflections

5. DO YOU SEE MATH IN THIS PICTURE?

6. What about this one?

7. How about now?

11. Pre-Image And Image
Pre-Image is the original figure before any type of transformation takes place.
Image is the new figure after the transformation has taken place.

12. Vocabulary
Isometry: a transformation in which the original figure and it’s image are congruent.
Opposite Orientation: when an image appears to be backwards compared to the pre-image.

13. Reflection
A transformation in which a line of reflection acts as a mirror reflecting points from their pre-image to their image.

14. Reflections A reflection reverses orientation.
A reflection is an isometry.
A reflection over the x-axis results in a change in the y-coordinate.
A reflection in the y-axis results in a change in the x-coordinate.

15. Reflections in Coordinate Plane
When reflecting a point over the x-axis the y-coordinate changes sign. (x, y)  (x, -y)
When reflecting over the y-axis the x-coordinate changes sign.
(x, y)  (-x, y)
When reflecting over the origin both the x and y coordinates change signs. (x, y)  (-x, -y)

16. Examples
If you reflect the point (6, -1) over the y-axis what would your new point be?
If you reflect the point (-2, 3) over the x-axis what would your new point be?
Reflect (-2, 4) over the origin. What is your new point?
Answers
(-6, -1)
(-2, -3)
(2, -4)

17. Translations

18. Translations
A translation is a sliding of a figure from one point to another. Since a sliding of a figure would not change the figures shape or size it is known as a Rigid Motion.

19. Vocabulary
Translation: is a transformation where you are sliding the object without changing orientation.
* A translation is an isometry
Composition: is when two transformations are performed one right after the other.

20. Examples of Translation
To perform a translation simply add or subtract from the coordinates of each point on the figure.
If we want to translate the point (4, 6) up 4 and left 3. We would simply add 4 to the “y” and subtract 3 from the “x”. We would get the new point (1, 10).

21. Translation
To translate a point in a coordinate plane simply add or subtract to the x or y coordinates.
To move the point (2, 4) up 3 units you would have to add 3 to the y-coordinate (4). So (2, 4) would become ( 2, 4 + 3) or (2, 7)

22. Vector Notation
Vector notation is used to show what you are doing to each coordinate to get your new coordinates.
The vector mean you subtract 3 from the x-coordinates and add 5 to the y-coordinates in order to get your new points.

23. Vocabulary
Glide Reflection: a glide reflection is simply when you translate a figure as well as reflect it over a line.

24. Rotation
A rigid motion that moves a geometric figure about a point known as the turn center.

25. Properties of a Rotation
A rotation is an Isometry.
A rotation does not change orientation.

26. Finding The Angle Of Rotation
Find the number of congruent images under a rotation and then divide that number into 360.
EX:
The image has 4 congruent views, so 360/4 = The image has a 90o angle of rotation.

27. Rotation of 180 Degrees
A Rotation of 180 Degrees about the origin, is equivalent to a reflection over the origin.
(x, y) becomes (-x, -y)

28. Examples
What would be the new point formed when you reflect the point (-2, 8) over the origin?
If you translate the point (-1, -4) using the vector , what would be the new point?
If the coordinates of A are (4, -2) and the coordinates of are (-2, 3) what vector was used to get the new point?