1) The net shown folds to a cube with a missing face. Mark with an x two edges where the final square can be placed so that the
net will fold to a cube with no missing faces.
|
Start from face #1 and start folding.
- Face 1 folds up under face 2
- Face 3 folds around the side of face 2
- After face 3 is folded, face 4 then folds down to make a top
- Face 5 then folds down, making the face opposite face 2
- This leaves the face to the left of face 2 open, so the final face can be placed in any of 4 positions:
- To the left of face 2
- To the left of face 1
- On top of face 4
- On top of face 5
The figure to the left shows what that folded net looks like from several perspectives:
|
2) The points A(1,3), B(2,3), C(2,2), D(0,0) and the origin are the vertices of a quadrilateral. Reflect ABCD across the line y = x. Reflect the resulting image A'B'C'D across the line y = 0 to get quadrilateral
A''B''C''D. What are the coordinates of A''?
|
The figure to the right shows the original position of A (the other coordinates don't matter), the reflect line y=x, the reflect line y=0 (the x axis) and the positions of A' (A after the reflection around y=x) and A'' (the position of A' after reflecting around y=0. The position of A'' is
(3,-1)
|
