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A regular octagon with three shaded sectors, joined at its lower right to a hexagon with two shaded sectors, beside a vertical dotted mirror line on the right

For the picture shown above, which one of the following is the correct picture representing reflection with respect to the mirror shown as the dotted line?

  • A.Octagon shaded at its upper right and lower left, joined at its lower left to a hexagon shaded at its upper left
  • B.Octagon shaded at its left and upper right, joined at its lower left to a hexagon shaded at its top
  • C.Octagon shaded at its top left, left and right, joined at its lower left to a hexagon shaded at its right side
  • D.Octagon shaded at its top left and top right, joined at its lower right to a hexagon shaded at its upper right

Answer: A

The correct reflection is (A).

A mirror on a vertical line swaps left and right and keeps up and down. In the original, the hexagon sits at the lower right of the octagon, so in the image it must sit at the lower left. The octagon's shaded sectors, which point to the upper left, to the left and to the lower right towards the hexagon, must point to the upper right, the right and the lower left. The hexagon's shaded sectors, on its right side, must move to its left side.

Picture (A) has all of these. (D) leaves the hexagon at the lower right, where it was before reflection. (B) and (C) put the hexagon on the correct side, but their shaded sectors are not the mirror images of the original ones: in (C) the hexagon's shading stays on its right, and in (B) the octagon keeps a shaded sector on its left away from the hexagon.

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