Figure ABCD is a rectangle with point A (-2, 5). What rule would rotate the figure 90° clockwise, and what coordinate would be the output for point A'?

Question

anonymous · Answer

(x,y)→(y,-x); A' (5, 2)

 (x,y)→(y,x); A' (5, -2)

 (x,y)→(-y,x); A' (-5, -2)

 (x,y)→(-y,-x); A' (-5, 2)

e.mccormick · Answer

Well, if you rotate clockwise, what happens?

e.mccormick · Answer

Lets say I start with this:
|dw:1404262677545:dw|

e.mccormick · Answer

Rotating 90 degrees would do something like this.  I put the lines in to show the 90 degrees.
|dw:1404262726921:dw|

anonymous · Answer

okay

anonymous · Answer

so it would be -5,2

e.mccormick · Answer

Sorry about that, got pulled away.  No.  See how on mine one of the values changes from a negative to a positive?  A 90 turn is always going to change the sign of something.

e.mccormick · Answer

In no two quadrants are both the x and y the same sign as each other.  So 90 degrees in either direction will cause change(s) in sign(s).
|dw:1404265029215:dw|

anonymous · Answer

so what would be answer be?

e.mccormick · Answer

Well, yours started in quad 2 and rotates to quad 1, so the - becomes +.  BUT, notice how the values change.  Look at my rough sketch.

|dw:1404265983176:dw|

If it starts there with (-2,5) where does it look like it ends at?

anonymous · Answer

5,3?

e.mccormick · Answer

Well, it is just a rough diagram.  It is not meant to be 3... (5,2).  You can test that with other points.  All you need is a piece of graph paper and anything with a 90 degree corner.  You can draw random 90 degree angles that are centered at and roughly equal lengths from the origin.  

You will find that they ALL do the same sort of shift where the x and y swap and sign changes on a certain one of them.  From that you can develop the basic rule that is part of the answer.