1. Final Review Slides
The following set of slides are designed to review the topics that will be on the final assessment.
Topics will include reflections, rotations, translations, and angles.

2. Rotations
When we rotate a figure we have to identify what point we are rotating it from and then in which direction we are rotating it. A complete rotation around the circle is 360 degrees.

3. Rotations
Assuming the far right point of the triangle which is at point (5,0) is rotated to the left or counter clockwise 90 degrees we arrive at point
5,5.
This is
a -90 deg.
rotation.

4. Reflections
When reflecting a figure we can do that over the x axis, y axis or both. *When you reflect over the x axis the y value is change. When you reflect over the y axis the x value is change. When you reflect over the x and y both values are changed.
Coordinate
Original (2,3)
Reflect y axis (-2,3)
Reflect x and y (-2,-3)
Reflect x axis (2,-3)

5. Reflections You can also do this with a shape. For example a triangle
Coordinate
Original (1,1) (3,1) (2,4)
Reflect y axis (-1,1) (-3,1) (-2,4)
Reflect x & y (-1,-1) (-3,-1) (-2,-4)
Reflect x axis (1,-1) (3,-1) (2,-4)

6. You can organize your coordinates into a table
Original (1,1) (3,1) (2,4)
Reflect y axis (-1,1) (-3,1) (-2,4)
Reflect x & y (-1,-1) (-3,-1) (-2,-4)
Reflect x axis (1,-1) (3,-1) (2,-4)
Reflect X Quadrant 2 X Y -1 1 -3 -2 4
Original Quadrant 1 X Y 1 3 2 4
Reflect x & y Quadrant 3 X Y -1 -3 -2 -4
Reflect y Quadrant 4 X Y 1 -1 3 2 -4

7. Practice. Fill out the missing areas. Original ( , ) ( , ) ( , )
Reflect y axis ( , ) ( , ) ( , )
Reflect x & y ( , ) ( , ) ( , )
Reflect x axis ( , ) ( , ) ( , )
Reflect X Quadrant 2 X Y
Original Quadrant 1 X Y
Reflect x & y Quadrant 3 X Y
Reflect y Quadrant 4 X Y

8. Translations
Translations are just moving a figure from place to the other.
We are use to seeing coordinate
given as (x,y).
When we communicate about a move
of the x, y we use (h,k).
The h is the movement on the x axis.
The y is the movement on the y axis.
A negative in front of the h or k indicates a move to the left on the x axis and down on the y axis.
A positive value indicates a move to the right on the x axis and a move up on the y axis.

9. Translate the triangle using a value of (-4, -6) as the (h,k)
Original ( 3, 1) ( 5 ,1) (4 , 4 )
Add the (h,k) + (-4,-6) (-4,-6) (-4,-6)
New location ( -1,-5) (1, -5 ) (0 ,-2)
Original Quadrant 1 X Y 3 1 5 4
Translation = Move X Y -1 -5 1 -2

10. Translate the triangle using a value of (5, -5) as the (h,k)
Practice
Translate the triangle using a value of (5, -5) as the (h,k)
Original ( , ) ( , ) ( , )
Add the (h,k) + ( , ) ( , ) ( , )
New location ( , ) (, ) ( , )
Original Quadrant 1 X Y
Translation = Move X Y

11. Supplementary Angles
Supplementary Angles are two angles that together add up to 180 degrees. *The angles do not have to be next to each other to be supplementary.
For example 45 degrees and 135 degrees add up to 180 degrees so they are supplementary angles.
45 degrees degrees = 180 degrees

12. Complementary Angles
Complementary Angles are two angles that add up to 90 degrees.
For example 20 degrees and 70 degrees add up to 90 degrees. *The angles do not have to be next to each other to be complimentary.
= 90 degrees

13. Vertical Angles
Vertical Angles are the angles opposite each other when two lines cross.
The two opposite angles are equal with respect to degrees. It creates to pairs of vertical angles.
135

14. Practice
Identify two complementary angles, two supplementary angles, two vertical angles. Identify one vertex.
135 C B E D A

15. Practice
Find the missing angle. * Remember that the vertical angles will add up to 360 degrees. This will help you.
Is there a complementary angle in this case?
Is there a supplementary angle in this case?
Why or why not? ?
140 C B E D A

16. Practice
Find the missing angle. * Remember that the vertical angles will add up to 360 degrees. This will help you.
Is there a complementary angle in this case?
Is there a supplementary angle in this case?
Why or why not? X +40 40 C B E D A