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hugsandkisses 3 years ago 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

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1. TuringTest

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

2. hugsandkisses

I wonder what that means too!

3. TuringTest

pretty sure meverett will tell you

4. meverett04

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

5. hugsandkisses

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

6. meverett04

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

7. TuringTest

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...

8. hugsandkisses

Oh, I see

9. meverett04

Why does this work Turing?

10. TuringTest

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

11. TuringTest

I will show you the actual formula...

12. hugsandkisses

thankyou

13. TuringTest

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

14. hugsandkisses

Haha, alright. thanks for trying though

15. TuringTest

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

16. TuringTest

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

17. hugsandkisses

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

18. TuringTest

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

19. hugsandkisses

thanks again for trying sir!

20. meverett04

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

21. TuringTest

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

22. TuringTest

not the matrices The part with the arrows

23. hugsandkisses

the arrows thing was much easier, thanks a ton

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