Transformations (AQA A-Level Further Maths): Quizzes

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Transformations
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For an enlargement with scale factor kk, what replaces xx and yy in the original equation?

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

What happens to a curve when enlarged by scale factor kk where k>1k > 1?

The curve becomes larger

For a rotation by π2\frac{\pi}{2} radians anticlockwise, how do xx and yy transform?

Replace xx by yy and yy by −x-x

For a rotation by π\pi radians about the origin, what substitutions are made?

Replace xx by −x-x and yy by −y-y

For a rotation by 3π2\frac{3\pi}{2} radians anticlockwise, how are variables replaced?

Replace xx by −y-y and yy by xx

In general rotation formulae through angle θ\theta, what is XX equal to?

xcos⁡θ+ysin⁡θx\cos\theta + y\sin\theta

When applying multiple transformations to a curve, what is crucial to remember?

The order matters

For a translation by vector (ab)\begin{pmatrix} a \\ b \end{pmatrix}, what replaces xx and yy?

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

When rotating a conic, how do asymptotes transform?

In the same way as the curve itself

To identify transformations from an equation, what should you do first?

Rearrange into standard form

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