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did i do this incorrectly?

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The problem states that this matrix:

$$\begin{bmatrix} 0 && -1 \\ 1&& 0 \end{bmatrix}$$

is multiplied by this matrix: (these are the vertices of a parallelogram btw the first row represents the x coordinate the second represents the y coordinate and the colums each represent a point: a,b,c...etc.
$$\begin{bmatrix} 5 &3&0& -2 \\ -2 &2&0&4 \end{bmatrix}$$

However when I did the work.....
This was my resulting matrix:
$$\begin{bmatrix} 2&-2&0&-4\\ 5&3&0&-2 \end{bmatrix}$$

The key however when i came to check my answer said the answer was some other matrix and that the parallelogram had this transformation:
a 270 degree rotation about the origin

However I said:
a 90 degree rotation about the origin.....

Did i do something wrong? if yes, can someone please explain what i did wrong :0

thank you so much!

Nov 15, 2019

#1
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Oof haven't learned matrices yet...

Welp I can only solve some competition problems,

Nov 15, 2019
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A 90 °  rotation clockwise  about the origin  has  the tranformation formula :

(x, y) ⇒ (  y, -x)

So

(5 , -2) ⇒ ( -2, -5)     which isn't correct

A  270° rotation clockwise about the origin  has  the transformation formula  :

( x , y) ⇒  (-y , x)

So

(5, -2) ⇒  ( 2 , 5)

(3, 2) ⇒  (- 2, 3)

(0, 0 ) ⇒ (0, 0)

(-2, 4)  ⇒ ( -4 , -2)

Here are the transformation rules, Nirvana :

https://quizlet.com/74135624/rotation-counterclockwise-reflection-coordinate-rules-flash-cards/

Nov 15, 2019
#3
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OK. Thank you, but I have a question.......since they told us to multiply by $$\begin{bmatrix} 0&& -1 \\ 1&& 0 \end{bmatrix}$$

shouldn't it be 90 degrees?

Nirvana  Nov 15, 2019
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The matrix for  a 90°  counter-clockwise rotation  is

[ 0   -1  ]

[ 1    0  ]

But this is the same as a 270° clockwise rotation

See the rotation matrices here : https://en.wikipedia.org/wiki/Rotation_matrix

Nov 15, 2019
edited by CPhill  Nov 15, 2019
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oh!
wait so now im confused........am i right or wrong.....

Nirvana  Nov 15, 2019
#6
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A 90 °  rotation clockwise  about the origin  has  the tranformation formula :

(x, y) ⇒ (  y, -x)

So

(5, -2)  would become ( -2, -5)

(3,2)  would become (2, -3)

(0,0)  would become (0, 0)

(-2, -4) would become ( -4, 2)

But your  transformed  points should be for a -90°  rotation  [ =  a 270°  rotation ]

(2,5)   (-2,3)  (0, 0)   and  ( -4, -2)

Which  are the points on your transformed matrix

CPhill  Nov 15, 2019
edited by CPhill  Nov 15, 2019
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on my paper i said 90 degrees counterclockwise which.............i thought that 90 degrees clockwise meant 270 degrees ccw and -90 meant 270 ccw

woah....what im so confused im so sorry )::::

Nirvana  Nov 15, 2019
edited by Nirvana  Nov 15, 2019
edited by Nirvana  Nov 15, 2019
#8
+109334
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See if this helps :

So    a 90°  counter-clockwise rotation  would put the vector  pointing up the y axis in a positive direction

The rotational matrix for  a 90° counter-clockwise rotation is the one you were given

But....this is the same thing as a 270°  clockwise rotation

Does this make sense  ???

Nov 15, 2019
edited by CPhill  Nov 15, 2019
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yes yes!! thank you so much CPhill!

Nirvana  Nov 15, 2019