If a mirror is placed on the line AB, then which of the answer figures is the…

2021

If a mirror is placed on the line AB, then which of the answer figures is the right image of the given figure?

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When a mirror is kept along a horizontal line such as AB drawn below a figure, every point of the figure is reflected straight across that line. The result is a vertical (up-down) flip of the whole figure: whatever sits at the top ends up at the bottom, and whatever sits at the bottom ends up at the top, while the left-right arrangement never changes. A plain square or block that is itself symmetric about a horizontal line through its centre looks the same after this flip. Any other mark -- a curved quarter-disc, a wedge, an outline, or a pentagon -- is not symmetric that way, so it still turns upside-down as part of the flip even though it stays just as solid or just as much an outline as before: a shape with a single point at the top and a flat base at the bottom (such as a point-up pentagon) must come out with a flat top and a single point at the bottom, not unchanged.

  1. Both bottom corners of the given figure are plain solid black squares. The top corners carry different marks instead: the top-left corner has a thin, unfilled hook-shaped outline, and the top-right corner has a solid, curved quarter-disc. After the flip, the two plain squares move to the top corners (unchanged in appearance, since a square is symmetric about a horizontal line through its centre), the hook outline moves to the bottom-left corner turned upside-down, and the quarter-disc moves to the bottom-right corner, its curve also turned upside-down.

  2. Inside the figure's inner square, the upper-left cell holds a solid black quarter-disc anchored at its own top-left corner, and the lower-left cell holds an unfilled pentagon outline that points upward (single point at top, flat base at bottom). After the flip these two cells swap, and each mark inverts: the pentagon outline moves up into the upper-left inner cell but now points downward (flat top, single point at the bottom), and the quarter-disc moves down into the lower-left inner cell, now anchored at that cell's bottom-left corner.

  3. On the right side of the inner square, the upper cell carries a black wedge with a diagonal line running to the centre, and the lower cell carries a black rectangle-and-notch block against the centre with its own diagonal line. After the flip, the rectangle-and-notch block moves up next to the centre divider and the wedge moves down, so the diagonal now bends the other way inside that column.

  • The figure whose bottom-left corner is filled solid black instead of showing an open hook has not inverted that mark correctly -- a solid fill cannot represent the flipped outline shape, so that figure is ruled out.

  • The figure whose upper-left pentagon still points upward, the same way as in the source figure, has left that mark unflipped -- a genuine reflection must turn it downward (flat top, point at the bottom), so that figure is ruled out even though its corners look right.

  • The figure whose pentagon and diagonal pattern sit on the opposite sides from the original (pentagon on the right, diagonal pattern on the left) has been mirrored left-to-right instead of flipped top-to-bottom, so that figure shows the wrong kind of reflection entirely.

  • Only the figure that keeps both top corners solid black, places the hook outline (correctly turned upside-down) at the bottom-left, places the quarter-disc curve at the bottom-right, shows the upper-left pentagon flipped to point downward, places the quarter-disc in the lower-left inner cell, and shows the rectangle-and-notch block swapped with the wedge on the right, satisfies every one of these checks.

That figure -- the one matching every one of these checks -- is the correct reflection of the given figure across line AB.

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