Question 1

Why doesn't it specify which way to turn, like 90 degrees clockwise or counterclockwise. I never heard of a -90 degree rotation. Any clarifications?

Accepted Answer

Counterclockwise angles are considered positive and clockwise are considered negative. Strangely the only KA video I can find mentioning this comes later in the Trigonometry series, but it should still be helpful: https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/Trig-unit-circle/v/unit-circle-definition-of-trig-functions-1

Question 2

How do you do this manually?

Accepted Answer

Apparently you're asking how would you do this not on KhanAcademy, but rotate a point using a pencil and paper?  For a simple rotation like 90 degrees you can just plot the points relative to the x-axis instead of y-axis.  For a more complicated rotation like 7 degrees, you'd need to use a protractor to measure the new angle.  Or if you're manually doing it on a computer you'd need to use the sine/cosine of the new angle to get the x & y coordinates, relative to the old angle.

Question 3

How do i do this with a pencil and a graph book

Accepted Answer

Rotation on paper, like the on at 0:30, can be done on paper. You do need a thumbscrew *compass* (note: this does not mean the navigational compass, but the drawing tool) and *protractor*, f.e. a set square with integrated protractor.
The process is a bit complicated. So I do a step by step explanation:
1.) Place the _needle point_ at the center of the rotation, in this case the origin of the coordinate plane. 
2.) Now _enlarge_ the compass, so that the pencil lead shows to the point you would like to rotate.  
3.) _Draw a circle._ So this would be a circle with the middle at the center of rotation  and the point somewhere on the circular line.
4.) _Draw a line_ from the original point to the center. 
5.) Now you need to find the rotated point. You need your rotation angle, in this case 90°. _Measure the rotation angle_ from the line in 4.) with the protractor. 
6.) _Draw a second line_ from the middle with the angle from 5.) to the first line.
7.) _Draw a point_ at the intersection of your line from 5.) and the circular line from 3.). This is your rotated pint.
8.)  _Repeat_ steps 1-7 for for the other point or if you would have a more complex figure for all remaining points. 
8.) _Connect_ the points and your are done.

Sorry for this complicated explanation. As a none native speaker a still have my problems with the proper english words for  certain mathematical procedures.

Question 4

Where did the name math come from?

Accepted Answer

The word mathematics comes from the Greek μάθημα (máthēma), which, in the ancient Greek language, means "that which is learnt",[24] "what one gets to know", hence also "study" and "science", and in modern Greek just "lesson".——from Wikipedia.

Question 5

Why doesn't it tell you which way to turn it clockwise or counterclockwise. Is that even a thing, a 90 degree turn?

Accepted Answer

Positive rotations go counterclockwise.
Negative rotations go clockwise.

Question 6

So is it true that we have to use formulas to perform rotations? A lot of the comments are suggesting the use of formulas

Accepted Answer

It's true that you have to use it in the exercises or at least some of them.  There is also the little rotate tool at times.  If you know the numerical coordinates of something you can figure out what they will be after a certain rotation.  It is also possible to perform rotations at least approximately using just a compass and  a protractor in the physical world.

With the line segment problem, you can view the rotation about a certain point as being the center of the circles of the rotation.  Choose one of the endpoints to rotate first.  Create a circle which has the segment endpoint on it and the point being rotated about as the center.  The rotated point will lie on this circle.  The angle between the lines made by the two points on the circle and the center of the circle is the angle of rotation.  Repeat this process for the other endpoint.  Joining the two points creates the rotated line segment.

Question 7

Wouldn't it be alot harder if you didn't have a computer to rotate it for you? How would you even do that?

Accepted Answer

I'd use a compass and protractor.  I'd draw two circles to start with, both centered at the origin, with the outer edge being one of the line segment endpoints.  I'd use the protractor, putting the middle dot at the origin of a circle and 0 at one of the line segment endpoints then measure out the rotation angle and plot that point on the same circle.  After rotating both points I'd connect them to create the new line segment.

Question 8

How do I actually do this not just watch them do it?

Accepted Answer

Usually after a few videos with "play" symbols next to their titles in the left-hand menu you'll see a title with a star instead. Those are exercises. Not all the topics covered in videos here on KA have associated practice tasks yet.

Geometry (all content)

Course: Geometry (all content) > Unit 10

Performing rotations (old)

Want to join the conversation?

Video transcript