Concepts · Figures
A turned figure keeps left as left. A mirrored one swaps left and right. One detail tells you which happened.
Kabir has a figure question in a mock test: which option is the F turned a quarter turn clockwise? Three of the options lie on their side, and two of them, a and b, both hang their arms down. He picks a.
It is wrong. Option a is not the F turned at all: it is the F flipped over, as a mirror would show it, and then laid on its side.
That evening his little sister, who is six, has her shoes on the wrong feet again. Kabir puts her right shoe on the floor in front of her. She turns it round and round on the floor, pointing the toe every way, trying to make it into a left shoe. However she turns it, it stays a right shoe.
Then she holds it up to the mirror in the hall. “Look! In there it’s a left one.”
Kabir laughs, then stops. That is his mock question. Turning never changes which foot a shoe fits; a mirror does. And he can tell which without trying it on: run a finger from the heel to the toe, and see which side the big toe is on. On her right shoe, seen from above, it is on the left, whichever way the toe points. In the mirror it is on the right.
A turn keeps left as left; a mirror swaps left and right. Pick two features and walk from one to the other, the way a finger runs from heel to toe, wherever they now point, and use the walker’s right and left, as if you were on a road. If a detail is on the same side as in the figure, it was turned. If it is on the other side, it was mirrored.
The test needs a figure with no line of symmetry: no fold matches its two halves. A plain square, or a dot set on a square’s diagonal, looks the same turned or mirrored, so the walk cannot tell them apart. A dot off every fold line, an F, a flag on one side of its pole: those it can. And flipping a paper figure over is a mirror, not a turn.
A water image flips a figure top to bottom instead of left to right. It is still a flip, so the walk catches it the same way: the detail moves to the other side. Option c in Kabir’s question was one.
Clocks in a mirror have a rule of their own: Mirror time.
At a glance, a turned option and a mirrored option can look alike, as Kabir’s a and b did. The walk turns “it looks right” into a check you can make on each option.
1. Which option is the figure turned, and not mirrored?
Walk from the foot of the pole, the end without the flag, to its top. Which side is the flag on?
Figure c
In the figure, walking from the foot of the pole to its top, the flag is on your right.
In figure c it is still on your right: a quarter turn. In a, b and d it is on your left: those are flips.
2. A mirror stands to the right of the figure. Which option is its image?
In a mirror at the side, up stays up. Only left and right swap.
Figure a
A mirror at the side flips the figure left to right: the long arm stays upright and the foot now points left.
Figure a. Figure c is flipped top to bottom, a water image; b and d are turns.
3. Three options are the same footprint, turned. Which one was made by the other foot?
Walk each footprint from the heel to the toes, as if on a road. Which side is the big toe on?
Figure c
In the figure, from heel to toes, the big toe is on your left.
In a, b and d it is still on your left: the same foot, turned. In figure c it is on your right: the other foot.
A week later, Riya tries him with one: a key with its teeth on one side, and four options. Two of them look the same at a glance. Kabir walks along each key from its ring to its tip. In one the teeth are on his right, as in the figure; in the other, on his left. He picks the first.
Non-verbal series is one of the app’s topics. Every question there is answered before its solution shows.
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