The Student Room Group

FP4 invariant lines

What actually is an invariant line? The points on the line move but the image of the line remains unchanged? How does that work?
Reply 1
Original post by Ano123
What actually is an invariant line? The points on the line move


An invariant line is one for which, under a given transformation, all points on the line are their own image. I'm not sure what you mean by them moving?
Reply 2
Original post by Zacken
An invariant line is one for which, under a given transformation, all points on the line are their own image. I'm not sure what you mean by them moving?


I do not think that is true
Reply 3
Original post by TeeEm
I do not think that is true


Fair. My description would be "a line of invariant points", right? I get confused. Don't even do this FP4 stuff. :colondollar:
Reply 4
Original post by Zacken
Fair. My description would be "a line of invariant points", right? I get confused. Don't even do this FP4 stuff. :colondollar:


yes

invariant line is one where points move but only on the line
line of invariant points, points do not move on that line
Original post by Zacken
Fair. My description would be "a line of invariant points", right? I get confused. Don't even do this FP4 stuff. :colondollar:


If a point is its own image, for all points, then you have the identity transformation. But an invariant line is one where a point on a line maps to a possibly different point on the line, as with a shear.
Reply 6
Original post by TeeEm
yes

invariant line is one where points move but only on the line
line of invariant points, points do not move on that line



Thanks! Apologies for the confusion OP, I'll let TeeEm take over. :smile:

Original post by Ano123
What actually is an invariant line? The points on the line move but the image of the line remains unchanged? How does that work?
Reply 7
Original post by Zacken
Thanks! Apologies for the confusion OP, I'll let TeeEm take over. :smile:


Noooo !!!

I am busy ,,,, !!!!

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