Flashcards · Maths · Transformations and Similarity
Combined Transformations
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What do two reflections in parallel lines give?
A translation, at right angles to the lines.
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How far is the translation?
Twice the distance between the mirror lines.
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What do two reflections in lines that cross give?
A rotation about the point where the lines cross.
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What is the angle of that rotation?
Twice the angle between the mirror lines.
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What single transformation is reflection in both axes?
A rotation of \(180^\circ\) about the origin.
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Where does \((x, y)\) go after reflection in \(y = x\) then the \(x\)-axis?
\((y, -x)\).
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What is an invariant point?
A point that does not move under a transformation.
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Which points are invariant in a reflection?
Every point on the mirror line.
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What is the invariant point of a rotation?
The centre of rotation.
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Does a translation have an invariant point?
No.
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How do you find the single transformation for a combination?
Compare the first shape with the last.
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Why label each shape \(A\), \(B\) and \(C\)?
It keeps the working clear and shows the order.
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Is the final image of a combination congruent to the object?
Yes, if the transformations are reflections, rotations and translations.
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Does the order of two transformations always matter?
Sometimes it does, so do them in the order given.
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What is the single transformation for two \(90^\circ\) clockwise rotations about the same centre?
A rotation of \(180^\circ\) about that centre.
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What is a combined transformation?
One transformation followed by another.