What's the formula for rotating on object over the origin?

Question

On a coordinate plane.

Can someone give me the formulas for 90 and 180 degree rotations both clockwise and counterclockwise around the origin?

Answer 1

to rotation 90° clockwise multiple R90 with vector X



| 0 -1|  

| 1  0|  =R90

| -1 0 |

| 0  -1| = R180

| 0 1 |

|-1 0 | = R270

counterclockwise is the same just R90 is R270c  and R270 is R90c

Answer 2

I'm not sure I understand the question. But, if you wanted to rotate a vector 90 or 180 degrees there are a few formulas that will work...

Making y=-y and x=-x in a cartesian coordinate system will reflect it across both axes, which is the same as rotating it 180°

Making y=-x and x=y would rotate 90°

Test this out to make sure.

Answer 3

90° clockwise: (x,y)→(y,-x)

90° counterclockwise: (x,y)→(-y,x)

180°: (x,y)→(-x,-y)