Invariant Points & Lines (Edexcel A-Level Further Mathematics): Flashcards

Point with coordinates unchanged after transformation

$Mmathbf{x} = mathbf{x}$

Line where points transform to other points on same line

$y' = mx' + c$

Set $Mmathbf{x} = mathbf{x}$ and solve two equations

A specific invariant point

A line of invariant points

$y = mx + c$

Points unchanged; lines map to themselves (points change)

Simplifies to specific invariant lines