1.True or false: Any sequence of rigid motions preserves the size of the transformed figure
A. This statement is false. Only sequences of rigid motions that do not include translations preserve the size of the transformed figure.
B. This statement is false. Only sequences of rigid motions that do not include reflections preserve the size of the transformed figure.
C. This statement is true.
D. This statement is false. No sequence of rigid motions preserves the size of the transformed figure.
5. Determine the mapping for transforming the point (x,y) by reflecting about the line y=x, rotating 180°, and then translating 4 units down and 5 units to the right.
A. (−y−5,−x+4)
B. (y+5,x−4)
C. (−y+5,−x−4)
D. (−y−5,−x+4)
answer all of them
1. B. This statement is false. Only sequences of rigid motions that do not include reflections preserve the size of the transformed figure.
5. A. The mapping for reflection about the line y=x is (y,x). The mapping for rotating 180° is (-x,-y). The mapping for translating 4 units down and 5 units to the right is (x+5,y-4). Therefore, the total mapping is (x+5,-y-4). When we reflect (x,y) about the line y=x, we get (y,x), then when we rotate using this (y,x) we get (-x,-y), then when we translate we get the final point (x+5,-y-4).