Answer:
see the attachment
Step-by-step explanation:
17. The two transformations you are to apply are ...
- translation: (x, y) ⇒ (x -3, y -3)
- reflecton: (x, y) ⇒ (y, x)
In the given order, the composite transformation is ...
(x, y) ⇒ (y -3, x -3)
In reverse order, the composite transformation is ...
(x, y) ⇒ (y -3), x -3)
Obviously, the composite transformation is the same when done in either order.
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The definition of a "glide reflection" is a translation followed by a reflection over a line. Since those are the transformations here, this is a glide reflection.
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Glide Reflection? — yes
Same in Reverse Order — yes
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18. The two transformations you are to apply are ...
- rotation: (x, y) ⇒ (-y, x) . . . . . counterclockwise 90°
- reflecton: (x, y) ⇒ (-x, y)
In the given order, the composite transformation is ...
(x, y) ⇒ (y, x) . . . . reflection across the line y = x
In reverse order, the composite transformation is ...
(x, y) ⇒ (-x, -y) . . . . reflection across the origin
Obviously, the composition of transformations is not the same when done in reverse order.
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Same in Reverse Order — no
Same as Reflection in y=x — yes
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The graph shows the transformations done by both problems. The dashed figure is the result of the first transformation. The final result is marked with the problem number next to the vertex letter.
