Thread: Transformation-rotation

Hello, mathhomework!

Draw with vertices: .

Find the coodinates of the vertices after a counterclockwise 90° rotation:

(a) about the origin. . (b) about . . {c} about . . (d) about

Luckily for both us, there are 90° rotations; there's a simple routine.


Suppose we have a point relative to a point

Code:

                    P
                    * (3,2)
                    ↑
                    ↑ 2
                    ↑
      O * → → → → → *
              3

Think of the slope of
. . That is, going from to , we move: .

Let be the new point after a 90° CCW rotation.

The slope of is perpendicular to
. . Hence: .

That is, going from to , we move: .


We know that will be northwest of
. . so we use the second fraction: .

From point , we move: .left 2, up 3.

Code:

            P'
            * (1,5)
            ↑
            ↑
            ↑ 3
            ↑
            ↑   2
            * ← ← ← * (3,2)
                    :
                    : 2
                    :
      O * - - - - - *
              3

And we arrive at: .



Do a few more of these and the steps will get smoother.
You'll come up with your own intuitive shortcuts.
Trust me on this . . .

Thank you!Thank you! Thank you! You are sooooo clear, I got it!

Please clear this up for me.

P rotates around O 90 degrees CCW, if I let O to be the origin, after the rotation P' will be (-2, 3) (I tried this and used tracing method.).

In your calculation, you didn't write the coordiantes of O. Does this mean O can be any point? But how come it does not work for (0, 0).

I looked at the tracing, the slopes of OP and OP' seem to perpendicular.

What did I do wrong?