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

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Invariant Points & Lines
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What condition must a point (x,y)(x, y) satisfy to be invariant under transformation matrix MM?

Mx=xM\mathbf{x} = \mathbf{x}

For a line to be invariant, where must transformed points lie?

On the same line

How many equations result from setting M(xy)=(xy)M\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} x \\ y \end{pmatrix}?

Two equations

What does a single solution when finding invariant points correspond to?

A specific invariant point

What do infinite solutions when finding invariant points describe?

A line of invariant points

What general line equation should you start with when finding invariant lines?

y=mx+cy = mx + c

What condition must the transformed y′y' satisfy for an invariant line?

y′=mx′+cy' = mx' + c

What two parameters do you solve for when finding invariant lines?

mm (slope) and cc (intercept)

What is a key difference between invariant points and invariant lines?

Points unchanged; lines may change points

What special case can simplify finding invariant lines?

c=0c = 0

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