Rotating a line anticlockwise about P

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Homework Help Overview

The problem involves finding the resulting equation of a line after it has been rotated anticlockwise by a specified angle about a given point using rotation matrices. The subject area pertains to linear algebra and geometric transformations.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of rotation matrices and the need to translate the line before and after the rotation. There are questions about understanding the rotation matrix and how to apply it to find the new line equation.

Discussion Status

Some participants have offered guidance on the steps needed to approach the problem, including translating the line and using matrix multiplication. There is an acknowledgment of the need for further understanding of matrix transformations, and additional resources have been shared for further exploration.

Contextual Notes

Participants express uncertainty about the rotation matrix and the process of translating the line, indicating a need for clarification on these concepts. There is a mention of seeking external resources for additional help.

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Homework Statement


Find the resulting equation of the line ax+by=c after rotating it anticlockwise by theta degrees about the point P(x0,y0) using the applications of the rotation matrix.


Homework Equations





The Attempt at a Solution

 
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you should be able to multiply it by a rotation matrix. Do you know what this is?
 
not really.. i need the equation of the new line though. I'm not quite sure how to go about this.. please help?
 
you need to translate the line so that its origin is at (x0, y0) then rotate and then translate the line back. You should be able to multiply these different matrices to obtain one matrix. Does this make sense?

I think you should look up matrix transformations if you still don't understand.
 
oh okay thank you. do you have know of a site at all that i may be able to refer to for extra help ?
 
http://wally.cs.iupui.edu/n351/3D/matrix.html

hope it helps
 
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