Rotating Vectors: Clockwise and Anti-clockwise

[lioric]

Homework Statement

I'm not asking how to do this question
This is a work done by one of my students
And the highlighted part it seems to be the correct answer that the teacher gave. I cannot make any sense out of these two questions
Perhaps one of you might shed some light on to this.

Homework Equations

Clockwise 90^O is
| 0 1 |
|-1 0 |

And anti clockwise 90^O is
| 0 -1 |
| 1 0 |

And this is about the origin

I also know that the inverse transformation of a clockwise rotation is anti clockwise rotation

The Attempt at a Solution

[/B]
But inverse matrix of a clockwise 90^O about the point (5,-2) is = (-2,5) I don't understand

 

[tnich]

Homework Statement

View attachment 224728

I'm not asking how to do this question so please don't put this in the home work section
This is a work done by one of my students
And the highlighted part it seems to be the correct answer that the teacher gave. I cannot make any sense out of these two questions
Perhaps one of you might shed some light on to this.

Homework Equations

Clockwise 90^O is
| 0 1 |
|-1 0 |

And anti clockwise 90^O is
| 0 -1 |
| 1 0 |

And this is about the origin

I also know that the inverse transformation of a clockwise rotation is anti clockwise rotation

The Attempt at a Solution

[/B]
But inverse matrix of a clockwise 90^O about the point (5,-2) is = (-2,5) I don't understand

You need to do this in three steps.
1) A translation that moves the point (5, -2) to the origin,
2) a 90° clockwise rotation,
3) a translation that moves the origin to the point (5, -2).

 

[Ray Vickson]

Homework Statement

View attachment 224728

I'm not asking how to do this question so please don't put this in the home work section
This is a work done by one of my students
And the highlighted part it seems to be the correct answer that the teacher gave. I cannot make any sense out of these two questions
Perhaps one of you might shed some light on to this.

Homework Equations

Clockwise 90^O is
| 0 1 |
|-1 0 |

And anti clockwise 90^O is
| 0 -1 |
| 1 0 |

And this is about the origin

I also know that the inverse transformation of a clockwise rotation is anti clockwise rotation

The Attempt at a Solution

[/B]
But inverse matrix of a clockwise 90^O about the point (5,-2) is = (-2,5) I don't understand

Do not post images: just type out the question and the parts you are having trouble with. Your images are unreadable on my devices, so I would not be able to help, even if I was willing to do so.

You should read the "pinned" post "Guidelines for students and helpers", by Vela; it explains fully the desirability of typing instead of attaching. Of course, typing it out requires some effort, but many (not all) helpers will say that if you are not willing to do it they are not willing to help.

 

[lioric]

You need to do this in three steps.
1) A translation that moves the point (5, -2) to the origin,
2) a 90° clockwise rotation,
3) a translation that moves the origin to the point (5, -2).

I know that part
I mean I know how to use matrix to find coordinates other that the origin

I'm just asking about the answer written by the teacher in that attachment
Cause I don't get how the numbers in the point of origin flips

 

[tnich]

You need to do this in three steps.
1) A translation that moves the point (5, -2) to the origin,
2) a 90° clockwise rotation,
3) a translation that moves the origin to the point (5, -2).

Since you are dealing with column vectors, it seems to me that your rotation matrices are backwards. If you apply the rotation matrix
$\begin{bmatrix} 0 & 1\\-1 &0\end{bmatrix}$

to a column vector
$\begin{bmatrix} a\\b\end{bmatrix}$

you get
$\begin{bmatrix} a'\\b'\end{bmatrix}=\begin{bmatrix} 0 & 1\\-1 &0\end{bmatrix}\begin{bmatrix} a\\b\end{bmatrix}=\begin{bmatrix} a\\b\end{bmatrix}$

I know that part
I mean I know how to use matrix to find coordinates other that the origin

I'm just asking about the answer written by the teacher in that attachment
Cause I don't get how the numbers in the point of origin flips

Seriously? That's the teacher's answer sheet? I don't think the answers to questions 13 and 14 make any sense at all.

 

[lioric]

Since you are dealing with column vectors, it seems to me that your rotation matrices are backwards. If you apply the rotation matrix
$\begin{bmatrix} 0 & 1\\-1 &0\end{bmatrix}$

to a column vector
$\begin{bmatrix} a\\b\end{bmatrix}$

you get
##\begin{bmatrix} a'\\b'\end{bmatrix}=\begin{bmatrix} 0 & 1\\-1 &0\end{bmatrix}\begin{bmatrix} a\\b\end{bmatrix}=\begin{bmatrix} a\\b\end{ts

Seriously? That's the teacher's answer sheet? I don't think the answers to questions 13 and 14 make any sense at all.

There it is
See ? that's what I m asking
It doesn't make any sense to me either
I was just asking you guys before I go nut thinking about this
Ya seriously why would the point of rotation flip like that
So can we agree that the answer to 13 and 14 are incorrect?