How are the coordinates of the new point found if it is rotated 90° counterclockwise? How many degrees is that equivalent to if the rotation is clockwise?

Question

nvidiaintely · Answer

@Kevin

kevin · Answer

360-90 = 270

nvidiaintely · Answer

How are the coordinates of the new point found if it is rotated 180° counterclockwise? How many degrees is that equivalent to if the rotation is clockwise?

will.h · Answer

am too bored seriously and too lazy i will just watch Kevin solving problems

nvidiaintely · Answer

lol

kevin · Answer

okay...
for the first question
we should find the matrix rotation 

$$M = \frac{ \cos180 \times -\sin180 }{ \sin 180\times \cos 180 }$$
$$= \left[\begin{matrix}-1 & 0 \ 0 & -1\end{matrix}\right]$$

so, for any (x,y) rotated by 180 degree would be 
$$(x,y) \times \left[\begin{matrix}-1 & 0 \ 0 & -1\end{matrix}\right]$$
= (-x, -y)

will.h · Answer

I wonder what's he typing. i never seen him typing like that before

kevin · Answer

I was typing the equation will.... lol

will.h · Answer

lol i will just watch.. looks pretty nice work keep going mate

kevin · Answer

wait,, it's 90 degree

kevin · Answer

OMG I'm writing again o_O

will.h · Answer

i don't think you needed to use all that tri functions

kevin · Answer

You have more simple method?

will.h · Answer

well there's simple form

90 degrees counterclockwise (x,y) --> (-y,x) that's a constant fact you don't need to prove anything

kevin · Answer

lol..
Honestly, my teacher never teach me like that xD
He just give me the matrix rotation formula..

Thx anyway will!

will.h · Answer

lol sure np 
your teacher loves to show off lol

kevin · Answer

xD