I'm a bit stuck on this. I need an explanation and solution

Question

There is a graph but I cannot attach so here are the points:

(2, 2) (2, 5) (3, 4) (4, 1)

-Rotate MNOP 90 degrees clockwise about the origin

-Show how to represent the rotation using matrices

-What are the coordinates of M' N' O' P'

Answer 1

So Lil H.,

Try to figure this out, bit by bit, by using model points. So if you rotate (1,0) by 90 degrees clockwise around the origin, where does it end up? You had better get (0, -1)! So what happened there? The x and the y exchanged and the value that exchanged reversed sign. Now do the same for (0, -1). You get (-1, 0). The x and y exchanged but they didn't reverse sign. Now do for (-1, 0): you get (0,1), again a sign reversal. And lastly (0,1): you get (1, 0), sign didn't reverse.

Now let's think what is the simplest way to say this, economically. When an x changes to a y, it flips sign == * -1, but when a y changes to an x, it preserves sign == * +1. You might want to try this on points like (1,2) and so on, to convince yourself that that's in fact what's true universally.

Now, you need a matrix way of expressing how to do this. I believe the way to conceive this is: each of x and y do NOT transform any of themselves into the rotation by 90 degrees clockwise. But the x to a y, needs a -1 matrix entry, and the y to an x, needs a +1 matrix entry. So maybe:

0 -1

1 0

Try that and see if it's that, or the other way around.

-- Cheers, --Mr. d.

P.S. When you start to do rotations by arbitrary #degrees, you will see that those matrix transforms use sin and cos functions, instead of just -1 and +1. Just sayin.