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!

Nirvana Nov 15, 2019

#1**0 **

Oof haven't learned matrices yet...

Welp I can only solve some competition problems,

CalculatorUser Nov 15, 2019

#2**+2 **

Your resulting matrix is correct

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/

CPhill Nov 15, 2019

#4**+2 **

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

CPhill Nov 15, 2019

#6**+1 **

Your answer was incorrect

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

#8**+2 **

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 ???

CPhill Nov 15, 2019