Transformations

[Dagenais]

This isn't really homework, but we are doing it in Geometry, and I'm having some trouble understanding it for some reason.

I know how easy it is supposed to be, but I'm having problems solving.

More specifically, with rotations.

Like say they give me coordinates on a coordinate plane, (x,y). 3 of these coordinates are given to make a quadrilateral.

And let's say they ask us to rotate it clockwise 90 and 180 degrees.

Counter-clockwise 260 degrees.

Is there anyway I can solve for that without moving my book around and making pencil marks all over my textbook?

Isn't the transformation suppose to be: (x,y) ---> (-y,x)?



[?]

[NateTG]

I'll give you some hints:

The formula for rotating points involves sin and cos.

If you can rotate <0,1> and <1,0> thought an angle of &theta; then <1,1> should be easy.

Perhaps this type of thing is easier in polar coordinates?

[HallsofIvy]

Are you sure it was 260 degrees? There is a general formula for any number of degrees but it is complicated and uses trigonometry.
Since the other examples you gave we 90 and 180, 270 degrees seems much more likely.

I like NateTG's suggestion. Start with the point (1,0). A 90 degree rotation moves it to (0, 1). A 180 degree rotation (another 90 degrees) takes it to (-1,0). A 270 degree rotation (three 90 degree rotations) take it to (0, -1). Now what happens to the point (a, 0) ("a" is some number) with each of those rotations?

Similarly, the point (0,1), rotated 90 degrees, becomes (-1,0), rotated 180 degrees, becomes (0, -1) and, rotated 270 degrees becomes (1,0). What do you think happens to (0,b) under those same rotations.

Now put them together. What happens to the point (a,b)?