1. 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?

2. Rotations

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

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

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

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

7. Symmetry Objective: Today, we will identify types of
symmetry in figures.

8. Reflectional Symmetry/Line Symmetry
A figure has reflectional symmetry if and only if a line coincides with the original figure.
The line is called the axis of symmetry.

9. Reflectional Line of Symmetry
A figure has reflectional symmetry if and only if there exists a line that “cuts” the figure into two congruent parts, that fall on top of each other when folded over the line of symmetry.

10. Rotational Symmetry
A figure has rotational symmetry of “n” degrees if you can rotate the figure “n” degrees and get the exact same image.
N must be between 0 and 360.

11. Point Symmetry
A figure has point symmetry when a rotation of 180 degrees maps the figure onto itself.
(It looks exactly the same upside down)

12. Examples
Name all the types of symmetry each figure has: (if rotational state how many degrees)
Rotational Symmetry (180)
Or Point Symmetry
Reflectional Symmetry (1)
Reflectional Symmetry (8)
Rotational Symmetry (45)

13. Alphabet Language Horizontal Line Vertical Line Rotational Symmetry
ENGLISH
(Uppercase)
GREEK

14. Greek Alphabet