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Rotation problem [duplicate]

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0

1

$begingroup$

This question is an exact duplicate of:

• 
  Rotation of an angle that has another as the center
  
  2 answers
  
  

With a 2D surface, we take $(2, 1)$ as the center point and consider a transformation with a rotation angle of $45^circ$ so point $(3, 3)$ is transformed into point?

I'm really close to getting the answer! I've gotten $(-1/sqrt2,3/sqrt2)$ but the answer is $(2-1/sqrt2, 3+1/sqrt2)$. Please tell me what I'm missing.

geometry trigonometry rotations

share|cite|improve this question

edited Mar 15 at 3:03

Parcly Taxel

44.7k1376109

asked Mar 15 at 2:52

JennYTJennYT

43

$endgroup$

marked as duplicate by Saad, Leucippus, Lord Shark the Unknown, mrtaurho, Vinyl_cape_jawa Mar 15 at 9:39

This question was marked as an exact duplicate of an existing question.

add a comment | 

0

1

$begingroup$

This question is an exact duplicate of:

• 
  Rotation of an angle that has another as the center
  
  2 answers
  
  

With a 2D surface, we take $(2, 1)$ as the center point and consider a transformation with a rotation angle of $45^circ$ so point $(3, 3)$ is transformed into point?

I'm really close to getting the answer! I've gotten $(-1/sqrt2,3/sqrt2)$ but the answer is $(2-1/sqrt2, 3+1/sqrt2)$. Please tell me what I'm missing.

geometry trigonometry rotations

share|cite|improve this question

edited Mar 15 at 3:03

Parcly Taxel

44.7k1376109

asked Mar 15 at 2:52

JennYTJennYT

43

$endgroup$

marked as duplicate by Saad, Leucippus, Lord Shark the Unknown, mrtaurho, Vinyl_cape_jawa Mar 15 at 9:39

This question was marked as an exact duplicate of an existing question.

add a comment | 

$begingroup$

This question is an exact duplicate of:

• 
  Rotation of an angle that has another as the center
  
  2 answers
  
  

With a 2D surface, we take $(2, 1)$ as the center point and consider a transformation with a rotation angle of $45^circ$ so point $(3, 3)$ is transformed into point?

I'm really close to getting the answer! I've gotten $(-1/sqrt2,3/sqrt2)$ but the answer is $(2-1/sqrt2, 3+1/sqrt2)$. Please tell me what I'm missing.

geometry trigonometry rotations

share|cite|improve this question

edited Mar 15 at 3:03

Parcly Taxel

44.7k1376109

asked Mar 15 at 2:52

JennYTJennYT

43

$endgroup$

share|cite|improve this question

edited Mar 15 at 3:03

Parcly Taxel

44.7k1376109

asked Mar 15 at 2:52

JennYTJennYT

43

share|cite|improve this question

edited Mar 15 at 3:03

Parcly Taxel

44.7k1376109

asked Mar 15 at 2:52

JennYTJennYT

43

edited Mar 15 at 3:03

Parcly Taxel

44.7k1376109

edited Mar 15 at 3:03

Parcly Taxel

44.7k1376109

asked Mar 15 at 2:52

JennYTJennYT

43

asked Mar 15 at 2:52

JennYTJennYT

43

1 Answer
1

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oldest

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1

$begingroup$

The displacement vector from $(2,1)$ to $(3,3)$ is $(1,2)$. Rotated counterclockwise by $45^circ$, $(1,2)$ becomes
$$beginbmatrix
cos45^circ&-sin45^circ\
sin45^circ&cos45^circ
endbmatrixbeginbmatrix1\2endbmatrix$$
$$=frac1sqrt2beginbmatrix
1&-1\1&1endbmatrixbeginbmatrix1\2endbmatrix=frac1sqrt2beginbmatrix-1\3endbmatrix$$
Thus $(3,3)$ is transformed to $(2,1)+frac1sqrt2(-1,3)$ or $left(2-frac1sqrt2,1+frac3sqrt2right)$.

share|cite|improve this answer

answered Mar 15 at 2:57

Parcly TaxelParcly Taxel

44.7k1376109

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you, are those matrices? How can I learn more about this topic?
  $endgroup$
  – JennYT
  Mar 15 at 3:44
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @JennYT They're rotation matrices. Look up Wikipedia for "rotation matrix".
  $endgroup$
  – Parcly Taxel
  Mar 15 at 3:45
  

  
  
  
  

add a comment | 

1

$begingroup$

The displacement vector from $(2,1)$ to $(3,3)$ is $(1,2)$. Rotated counterclockwise by $45^circ$, $(1,2)$ becomes
$$beginbmatrix
cos45^circ&-sin45^circ\
sin45^circ&cos45^circ
endbmatrixbeginbmatrix1\2endbmatrix$$
$$=frac1sqrt2beginbmatrix
1&-1\1&1endbmatrixbeginbmatrix1\2endbmatrix=frac1sqrt2beginbmatrix-1\3endbmatrix$$
Thus $(3,3)$ is transformed to $(2,1)+frac1sqrt2(-1,3)$ or $left(2-frac1sqrt2,1+frac3sqrt2right)$.

share|cite|improve this answer

answered Mar 15 at 2:57

Parcly TaxelParcly Taxel

44.7k1376109

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you, are those matrices? How can I learn more about this topic?
  $endgroup$
  – JennYT
  Mar 15 at 3:44
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @JennYT They're rotation matrices. Look up Wikipedia for "rotation matrix".
  $endgroup$
  – Parcly Taxel
  Mar 15 at 3:45
  

  
  
  
  

add a comment | 

1

$begingroup$

The displacement vector from $(2,1)$ to $(3,3)$ is $(1,2)$. Rotated counterclockwise by $45^circ$, $(1,2)$ becomes
$$beginbmatrix
cos45^circ&-sin45^circ\
sin45^circ&cos45^circ
endbmatrixbeginbmatrix1\2endbmatrix$$
$$=frac1sqrt2beginbmatrix
1&-1\1&1endbmatrixbeginbmatrix1\2endbmatrix=frac1sqrt2beginbmatrix-1\3endbmatrix$$
Thus $(3,3)$ is transformed to $(2,1)+frac1sqrt2(-1,3)$ or $left(2-frac1sqrt2,1+frac3sqrt2right)$.

share|cite|improve this answer

answered Mar 15 at 2:57

Parcly TaxelParcly Taxel

44.7k1376109

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you, are those matrices? How can I learn more about this topic?
  $endgroup$
  – JennYT
  Mar 15 at 3:44
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @JennYT They're rotation matrices. Look up Wikipedia for "rotation matrix".
  $endgroup$
  – Parcly Taxel
  Mar 15 at 3:45
  

  
  
  
  

add a comment | 

$begingroup$

The displacement vector from $(2,1)$ to $(3,3)$ is $(1,2)$. Rotated counterclockwise by $45^circ$, $(1,2)$ becomes
$$beginbmatrix
cos45^circ&-sin45^circ\
sin45^circ&cos45^circ
endbmatrixbeginbmatrix1\2endbmatrix$$
$$=frac1sqrt2beginbmatrix
1&-1\1&1endbmatrixbeginbmatrix1\2endbmatrix=frac1sqrt2beginbmatrix-1\3endbmatrix$$
Thus $(3,3)$ is transformed to $(2,1)+frac1sqrt2(-1,3)$ or $left(2-frac1sqrt2,1+frac3sqrt2right)$.

share|cite|improve this answer

answered Mar 15 at 2:57

Parcly TaxelParcly Taxel

44.7k1376109

$endgroup$

share|cite|improve this answer

answered Mar 15 at 2:57

Parcly TaxelParcly Taxel

44.7k1376109

answered Mar 15 at 2:57

Parcly TaxelParcly Taxel

44.7k1376109

answered Mar 15 at 2:57

Parcly TaxelParcly Taxel

44.7k1376109