Hello, mathhomework!

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 . . .