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Crazy boy [7]
3 years ago
5

A.) Describe a transformation sequence that will transform quadrilateral ABCD into quadrilateral A’B’C’D’.

Mathematics
1 answer:
Mariulka [41]3 years ago
8 0

a.) The orientation of ABCD is clockwise, as is the orientation of A'B'C'D'. This means the transformation involves a even number of reflections (may be 0). The orientation of AB is North, and the orientation of A'B' is West, so a rotation of 90° CCW (or equivalent) is involved. We can find the point of intersection of the perpendicular bisectors of AA' and BB' (at (-1, -1)) to determine a suitable center of rotation.

ABCD can be transformed to A'B'C'D' by ...

  • rotation 90° CCW about the point (-1, -1)

b.) Rotation by 90° can also be accomplished by reflection across a diagonal line. Since we want the orientation to remain unchanged, we need another reflection to put the figure into its final position. A suitable alternate sequence for mapping ABCD to A'B'C'D' is ...

  • reflection across the line y=x
  • reflection across the line x=-1

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