1. 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)

2. Translations

3. 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.

4. 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.

5. 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).

6. 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)

7. 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.

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

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

10. Finding The Angle Of Rotation
Find the number of congruent images under a rotation and then divide that number into 360.
EX:

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