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Assembling ObjectsLesson 3 of 3

Rotation, Reflection and Elimination

Rotation is allowed, reflection is not, and why eliminating beats constructing.

Table of ContentsShow
  1. What the rule is
  2. Telling them apart in seconds
  3. Why elimination beats construction
  4. The order to work in
  5. What you can skip
  6. Where people lose points
  7. Work one in under a minute
  8. Where this leads

Everything in the two format lessons comes back to one question that is worth being able to answer instantly: is the piece in front of me the piece I was given, or its mirror image?

What the rule is

Rotation keeps a piece the same piece. Turn it a quarter turn, a half turn, seventeen degrees, and it is still the piece you were given. An answer choice may show any of your pieces at any angle.

Reflection makes a different piece. Flip it over, and unless the piece happens to be symmetrical, what you have cannot be turned back into the original no matter how you rotate it.

This is easier to believe once you have watched every angle fail.

An L-shaped piece starts a quarter turn round and turns until it lands exactly on a dashed outline of itself: a turned piece is the same piece. Then the flipped version of the piece turns a full 360 degrees over the same outline and never fits at any angle: a flipped piece is a different piece.

So an answer choice containing a mirrored version of one of your pieces is wrong, and you can strike it without looking at anything else in it.

This is the rule the test writers lean on hardest, because a mirrored shape has the same edges, the same angles, the same area and the same outline complexity as the original. At a glance it looks right. Only handedness gives it away.

Telling them apart in seconds

Do not try to outline-match. The outlines are identical by construction and comparing them will not resolve anything.

Pick one asymmetric feature and check its handedness.

Step one: find a feature that is not symmetric. A notch, a point, the longer of two arms, a curve on one side.

Step two: fix its relationship to something else on the piece, in words. "The long arm goes down from the left-hand end of the short arm." "The notch is on the right of the long edge, with the point at the top."

Step three: check that relationship in the answer. Rotation preserves it, whatever angle the piece is drawn at. Reflection reverses it.

In the figure, the piece's long arm hangs down from the left-hand end of the short arm. In the "turned" panel, that relationship survives the turn. In the "flipped over" panel the long arm hangs from the right-hand end, and no rotation restores it.

Symmetrical pieces cannot be caught this way, and it is important to know that before you waste time trying. A square, a circle, an isosceles triangle and a rectangle are all identical to their own mirror images, so a reflection of one is also a rotation of it and there is nothing to detect. This is not a weakness in the method; it is a reason to pick your tracking piece deliberately. Reach for the asymmetric piece every time, both because it is the only one that can catch a reflection and because it is the piece the error is most likely to be hiding in.

Why elimination beats construction

The clock decides this. The computer version allows roughly seventy-two seconds a question; on paper it is about thirty-six.

Constructing the right answer means assembling a figure in your head and comparing it with four candidates. For anything past three or four pieces that is slower than the time available, and it fails silently: you finish the assembly, it half matches two options, and you have spent the whole question.

Eliminating means looking for one fault in each choice. Each wrong option typically carries exactly one, deliberately - a mirrored piece, a shape with the wrong number of sides, a connection point moved to a corner, a piece count that does not work.

Three eliminations leave one answer, and you never had to know why it was right.

The order to work in

One: scan for mirrored pieces. Fastest to spot once you know how, and the most commonly planted fault.

Two: scan for wrong or missing shapes, and for the wrong piece count. Both need no precision.

Three: check attachment points or the distinctive piece on whatever survives.

Four: if two survive, find the one difference between them. There is always exactly one, and it is what the question was about.

Five: choose and move on. A question you have spent ninety seconds on has already cost you more than it can pay.

One more thing worth saying plainly, because it changes how much of this applies to you. For an Air Force applicant, Assembling Objects feeds no AFQT score and none of the four Air Force line scores. It is the only subtest on the ASVAB that cannot open or close a career field for you. Learn the mirror rule and the elimination order, because together they take twenty minutes and will carry most of what this subtest can be carried by, and then put your study hours where they score. If you may also test for the Navy, which does use this score for some ratings, that calculation changes.

What you can skip

  • Mental rotation speed drills. Elimination on one clear feature is faster than rotating a whole shape in your head, and it is the method this lesson teaches.

Where people lose points

Matching outlines instead of handedness. A reflection has the same outline.

Tracking a symmetrical piece. It cannot reveal a reflection.

Assuming an unfamiliar angle means a reflection. Rotation is unlimited.

Constructing the answer instead of eliminating three. There is not time.

Re-verifying a choice you have already faulted. It is dead.

Giving this subtest study time that belongs to Arithmetic Reasoning.

Work one in under a minute

You are given an L-shaped piece whose long arm hangs down from the left-hand end of its short top arm. Answer choice A shows the piece with the long arm running right along the bottom and the short arm running down its left side. Choice B shows the long arm hanging down from the right-hand end of the short top arm. Which of these, if either, is a legal appearance of your piece?

A is legal. B is not.

Take A first. Turn the original piece a quarter turn and the short top arm swings down to become a vertical arm on the left, while the long arm swings from vertical to horizontal along the bottom. That is exactly what A shows, so A is the same piece, turned.

Now B. The relationship you were given is long-arm-from-the-left-hand-end. B shows long-arm-from-the-right-hand-end. Rotation cannot change which end of the short arm the long arm grows from, because rotation moves the whole piece together. Only flipping it over does that, and flipping is not allowed.

So B is a reflection, and any answer choice containing it is wrong regardless of everything else in that choice.

Note what settled it. Not the outline, which is the same in both. The relationship between two parts of the same piece, which is what handedness means and what rotation can never alter.

Where this leads

This closes Assembling Objects, and with it every lesson on the site. The mirror rule and the elimination order are what the two format lessons were built to use.

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