Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Mathematics
Linear and Abstract Algebra
Visualising transformations
Reply to thread
Message
[QUOTE="lemonthree, post: 6782005, member: 708903"] Given that [MATH] H_{1} [/MATH]= reflection about the line y = x + 1; [MATH]H_{2} [/MATH]= counterclockwise rotation of pi/2 about the point (1,0); [MATH]H_{3} [/MATH]= translation by 1 - i. What is the image of the triangle and arrow under the map [MATH] H = H_{1} *H_{2} * H_{3} [/MATH]? I need help visualising the above transformation H. I know that [MATH] H = H_{1} *H_{2} * H_{3} [/MATH], so we must perform the transformations from right to left (H3 first, then H2, and lastly H1). Now, in a question that provides the equation for [MATH] H_{1},H_{2} , H_{3} [/MATH], I believe I can solve this by substituting the values into [MATH] H_{1},H_{2} , H_{3} [/MATH] respectively. However, in this case, the question does not provide the equation and it is up to my visualisation. I have attached photos showing my steps for each respectively. I have no trouble with translation (H3) as it is relatively easy to visualise. However, I struggle a little for the rotation about (1,0). I can't quite visualise "pivoting" the arrow and triangle about (1,0)...I would like to ask for some tips to aid in visualising such rotations better. [/QUOTE]
Insert quotes…
Post reply
Forums
Mathematics
Linear and Abstract Algebra
Visualising transformations
Back
Top