Question

Quadrilateral WXYZ is located at W(3, 6), X(5, -10), Y(-2, -4), Z(-4, 8). A rotation of the quadrilateral is located at W�(-6, 3), X�(10, 5), Y�(4, -2), Z�(-8, -4). How is the quadrilateral transformed?
A. Quadrilateral WXYZ is rotated 90º counterclockwise about the origin
B. Quadrilateral WXYZ is rotated 90º clockwise about the origin
C. Quadrilateral WXYZ is rotated 180º about the origin
D. Quadrilateral WXYZ is rotated 45º about the origin

Answer 1

hmm...
it looks like all the coordinates are changing from\[(a,b)\to(-b,a)\]I wonder what that means.

Answer 2

I wonder what that means too!

Answer 3

pretty sure meverett will tell you

Answer 4

Draw a picture of the original shape. Then like the previous one, draw four circles for W, X, Y and Z. We have the 180 degree rotation again. C is our answer

Answer 5

I dont understand the rotations thing though. is there a formula, or do I have to draw everytime?

Answer 6

I am a visual learner, I draw the picture every time. @Turing, do you have a formula?

Answer 7

When you see the coordinates change from...
\[(a,b)\to(-b,a)\]that means.a means counter-clockwise rotation 90 degrees
clockwise is this change\[(a,b)\to(b,-a)\]the opposite of course.

180deg is\[(a,b)\to(-a,-b)\]which is obvious if you think about it.
So I guess I do...

Answer 8

Oh, I see

Answer 9

Why does this work Turing?

Answer 10

I can recall that only because I just did it yesterday
The real formula is done with matrices, but gives the same result.

Answer 11

I will show you the actual formula...

Answer 12

thankyou

Answer 13

you don't want it hugsandkisses it is above your level
sorry...

Answer 14

Haha, alright. thanks for trying though

Answer 15

this multiplication maps a vector onto itself:\[(a,b)\left[\begin{matrix}1 & 0 \\ 0 & 1\end{matrix}\right]\]...

Answer 16

this one turns it 180 degrees\[(a,b)\left[\begin{matrix}-1 & 0 \\ 0 & -1\end{matrix}\right]\]

Answer 17

umm.. thanks for trying to explain it to me :P

Answer 18

here is 90 deg closkwise\[(a,b)\left[\begin{matrix}0 & -1 \\ 1 & 0\end{matrix}\right]\]and counter-clockwise is\[(a,b)\left[\begin{matrix}0 & 1 \\ -1 & 0\end{matrix}\right]\]

Answer 19

thanks again for trying sir!

Answer 20

Hmmm ... I have some reading to due .... thank you for the start ...

Answer 21

but for you hugs and kisses just use what I gave above.
I actually gave you the answer is you put my posts together.

Answer 22

not the matrices
The part with the arrows

Answer 23

the arrows thing was much easier, thanks a ton