+700 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!
+2863 Oof haven't learned matrices yet...
Welp I can only solve some competition problems,
+129852 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/
+129852 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
+129852 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
+129852 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 ???
