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Problem 184

Geometry Difficulty 1.3 Multiple choice CEMC Pascal · Canada · 2014

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 $L$ . Which of the following shows the final position of the figure?

Pick one

Official solution

Solution 1

The square, its 8 pieces and 2 diagonals are symmetrical about line $L$ . Upon reflection, the circle moves from the triangular above $L$ which is adjacent to and above the second diagonal to the triangular region below $L$ 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 $45^\circ$ 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 $45^\circ$ ), we obtain the figure in (D).

Figure for this problem

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