1. Rotations
About the Origin
By Ishaq Chowdhury

2. Transformations can be pretty confusing
Reflection?
Dilation?

3. Especially when it comes to Rotations

4. Clockwise
Rotation

5. But maybe I can help explain it

6. Let’s Start With a Definition
A rotation about a point “P” through an angle, “X”
is a transformation such that:
1. the image of P is P
2. Any other point Q has the point Q’, where
PQ=PQ’ and <QPQ’=X

7. What does that even mean?
In simple english it means that everything
moves except the point you’re rotating around.
All the points move in a way that it stays the
same distance from center of the rotation as it
did before.

8. Usually a rotation occurs with the origin at the
center. Here are some rules for the most used
rotations.

9. A 90 degrees counter-
clockwise rotation is:
R90(x, y) to (-y, x)
The x coordinate and the y coordinate switch
places and the y is negated.

10. A 180 degrees
counter-clockwise
rotation is:
R180(x, y) to (-x, -y)
Both the x and the y coordinates are negated.

11. A 270 degrees
counter-clockwise
rotation is:
R270(x, y) to (y, -x)
The x coordinate and the y coordinate switch
the the x is negated.

12. If a figure is rotated clockwise:
The degrees of rotation becomes negative.
For example:
rotate 270 degrees clockwise
R-270(x, y)
This is the same as 90 degrees counter-clockwise
rotation.
so R-270(x, y) is (-y, x)

13. But when will we actually
ever need to know how to
rotate things in real life?

14. Let’s think:
Counter-CLOCKwise

15. The hands of a clock rotate
around the center to indicate
what time it is.

16. Lets say we have
our clock here.
The center of the
clock is at the origin.
The point of the hour
hand is at (0,2)

17. Rotating it 270
degrees would make it
3 o’clock.
Applying the rule:
R270(x, y)---(y, -x)
would change
(0,2) to (2, 0)

18. Rotating it 180
degrees from its
original point would
make it 6 o’clock.
Applying the rule:
R180(x, y)---(-x, -y)
would change
(0,2) to (0,-2)

19. Rotating it 90 degrees
would make it 9’clock.
Applying the rule:
R90(x, y)---(-y, x)
would change
(0,2) to (-2,0)

20. Now you have the final piece of information that you
need to rule the world!!!!!
Congrats!