Transformations (AQA A-Level Further Maths): Flashcards

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Transformations
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What transformations do

Change position, size, or orientation of curves

Three main types of transformations for conics

Enlargements, rotations, translations

Enlargement rule for scale factor kk

Replace xx with xk\frac{x}{k}, yy with yk\frac{y}{k}

Effect of scale factor k>1k > 1 in enlargement

Makes the curve larger

Rotation by π2\frac{\pi}{2} radians: substitution rule

Replace xx by yy and yy by −x-x

Rotation by π\pi radians: substitution rule

Replace xx by −x-x and yy by −y-y

Rotation by 3π2\frac{3\pi}{2} radians: substitution rule

Replace xx by −y-y and yy by xx

Translation by (ab)\begin{pmatrix} a \\ b \end{pmatrix}: rule

Replace xx with (x−a)(x-a), yy with (y−b)(y-b)

Order of multiple transformations

Order matters; apply sequentially

How asymptotes transform with the curve

Apply the same transformation rules to asymptote equations

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