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

2021

Q. 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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Attempted by 121 students.

Show answer & explanation

Concept

A plane mirror placed along a vertical line produces a lateral (left-right) inversion: every feature swaps to the opposite side of the line, while its height (top versus bottom) stays exactly as it was. For a striped figure this has two consequences: each diagonal hatch reverses its own lean (a line that slanted one way now slants the other way), and the vertical bands themselves reorder left-to-right in reverse - each band otherwise keeping its own top-to-bottom pattern unchanged.

Applying it to this figure

  1. Read the given figure as five vertical bands, left to right: a plain band that is white with a single dark block at its bottom; a band that is dark at its top and diagonally hatched below (that hatch leaning from bottom-left to top-right); the pentagons-and-shaded-circle band in the centre; a band that is diagonally hatched at its top and plain white below (that hatch leaning from top-left to bottom-right); and a plain band that is dark at both its top and its bottom with white in between.

  2. A left-right reflection reverses the order of these five bands and reverses each hatch's own lean, while every band keeps its own top-to-bottom pattern.

  3. So in the reflected figure: the band dark at both top and bottom (with white between) sits nearest the mirror line; next to it sits the band that is hatched at top and white below, but its hatch now leans bottom-left to top-right; the centre still reads pentagon, shaded circle, pentagon top to bottom, with the circle's shaded wedge now on the opposite side from the original; next sits the band that is dark at top and hatched below, but its hatch now leans top-left to bottom-right; and furthest from the mirror line sits the plain white band with its single dark block at the bottom.

Cross-check

Checking this against the given figure confirms two independent signals together: both hatch strips have genuinely reversed their own lean (not simply changed sides while keeping the same lean), and the two solid dark blocks sit on the corner diagonal opposite their original positions. The right image is the figure showing exactly that combination - a hatched-then-white band leaning bottom-left to top-right beside the band that is dark at both top and bottom, and a dark-then-hatched band leaning top-left to bottom-right beside the white band with a bottom block.

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