Answer to Question #132587 in Differential Geometry | Topology for amerie

Question

Bob claims that he can map Rectangle 1 to Rectangle 2.
Select THREE of the transformations or series of transformations that support his claim.
A
a translation of 2 units down followed by a 180° rotation about the point (1, 2)

B
a reflection over the line x = 0 followed by a reflection over the line y = 4

C
a reflection over the line x = 1 followed by a translation of 2 units down

D
a translation of 12 units right and 2 units down

E
a rotation of 180° about the point (1, 4)

F
a translation of 6 units right

Answer 1

The question needs a picture. Here it is

A. If we translate it by two points down, then the first rectangle will have the same y-coordinates as the second. Next, the rotation about (1,2) will transform it into the rectangle with y-coordinates from 0 to 2, so we can't obtain the second rectangle

B. The reflection over x=0 transforms it into rectangle in first quadrant with the abscissae from 2 to 8, but ordinates will be from 4 to 6. So the reflection over y=4 transforms it into the rectangle with abscissae from 2 to 8 and y-coordinates from 2 to 4, not equal to 2 rectangle.

C. The reflection over x=1 transforms it into rectangle in first quadrant with the abscissae from 4 to 10, but ordinates will be from 4 to 6. If we move it downwards by 2 units, we'll obtain the second rectangle.

D. The translation of 12 units right will make abscissae equal to values from 4 to 10, but y-coordinates will be from 4 to 6. If we move it downwards by 2 units, we'll obtain the second rectangle.

E. If we rotate the rectangle about (1,4), the point (-2,6) will transform into (4,2), the point (-2,4) will transform into (4,4). The first rectangle will transform into the second rectangle.

F. The translation of 6 units right will save y-coordinates equal to values from 4 to 6, so we can't obtain the second rectangle.