In the diagram, a figure is formed dividing a square into eight identical pieces using its two diagonals and the two lines joining the midpoints of opposite sides, and then drawing a circle in the square as shown.
This figure is reflected in line . Which of the following shows the final position of the figure?
(A) (B) [[IMAGE1]] (C) [[IMAGE2]] (D) [[IMAGE3]] (E) [[IMAGE4]]
Solution 1
The square, its 8 pieces and 2 diagonals are symmetrical about line .
Upon reflection, the circle moves from the triangular above which is adjacent to and above the second diagonal to the triangular region below which is adjacent to and above the second diagonal.
[[IMAGE0]]
Solution 2
We can see that the final position of the figure is given in (D) by first rotating the original figure by clockwise to obtain:
[[IMAGE1]]
Then, reflecting the figure through the now vertical line, we obtain: [[IMAGE2]] When we reposition the figure and line back to the original position (by rotating counterclockwise by ), we obtain the figure in (D).