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Flashcards · Maths · Transformations and Similarity

Combined Transformations

16 cards

  1. What do two reflections in parallel lines give?

    A translation, at right angles to the lines.

  2. How far is the translation?

    Twice the distance between the mirror lines.

  3. What do two reflections in lines that cross give?

    A rotation about the point where the lines cross.

  4. What is the angle of that rotation?

    Twice the angle between the mirror lines.

  5. What single transformation is reflection in both axes?

    A rotation of \(180^\circ\) about the origin.

  6. Where does \((x, y)\) go after reflection in \(y = x\) then the \(x\)-axis?

    \((y, -x)\).

  7. What is an invariant point?

    A point that does not move under a transformation.

  8. Which points are invariant in a reflection?

    Every point on the mirror line.

  9. What is the invariant point of a rotation?

    The centre of rotation.

  10. Does a translation have an invariant point?

    No.

  11. How do you find the single transformation for a combination?

    Compare the first shape with the last.

  12. Why label each shape \(A\), \(B\) and \(C\)?

    It keeps the working clear and shows the order.

  13. Is the final image of a combination congruent to the object?

    Yes, if the transformations are reflections, rotations and translations.

  14. Does the order of two transformations always matter?

    Sometimes it does, so do them in the order given.

  15. What is the single transformation for two \(90^\circ\) clockwise rotations about the same centre?

    A rotation of \(180^\circ\) about that centre.

  16. What is a combined transformation?

    One transformation followed by another.