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Mirror Image

Reasoning · Non-Verbal Reasoning

7 Part2 worked examples6 practice questions

Write something in your notebook and hold it in front of a bathroom mirror. The words look reversed, and the end of the line that was on your right appears on the left in the glass. That picture in the glass is the mirror image.

In the exam you get a figure with a mirror line drawn beside it and four options. You must choose the option that is the correct image of that figure. There is nothing to memorise; you only have to understand what a mirror changes and what it does not change.

Every question here is a picture: the question figure on top and the options A, B, C, D below it. Look at the picture, find the right figure and then press the button with the same letter (“Figure A” etc.). All figures are drawn from geometry by computer, so the answer given is measured, not guessed.

How to use this chapter

  1. Read — first the idea, then the way to spot it.
  2. Study the solved example — the “Example” boxes show the whole solution with a picture; the lower picture shows the figure, the mirror and the image together.
  3. Try it yourself — in “Try it yourself first” the solution is hidden. Look at the figure and decide, then choose an option.
  4. Know the level — Basic, Standard, Advanced; make the basic ones solid first.
NoteIf the pictures look small, turn the phone sideways or pinch to zoom. The questions you have solved are remembered in this browser.
1

Foundation — what a mirror does

Mirror line, flip and a three-step method

The vocabulary of images, which way a mirror flips and a three-step method for every question.

What an image is

Object, mirror line, image

The vocabulary of images and its three firm rules.

TermMeaningExample
ObjectThe thing whose image we wantThe letter F
Mirror lineThe place of the mirror, the thick line in the pictureA vertical line to the right of F
ImageThe picture seen on the other side of the mirrorA reversed F
Lateral inversionLeft and right changing placesA stem on the left appears on the right

Below, the letter F, the mirror line on its right and its image are drawn together.

F, the mirror line and the image of F

Three firm rules come out of this picture, and they work in every question:

  1. Size and shape do not change. The image is as big as the object; no part grows, shrinks or appears from nowhere.
  2. Distance stays equal. The part nearest to the mirror is also nearest to it in the image. The near-to-far order from the mirror stays the same.
  3. The direction facing the mirror reverses. What swaps is the direction in which the mirror stands (see the next part).

Try the “fold test” too: imagine folding the paper along the mirror line. Where the figure lands is the image. It lands on the other half of the paper, which is why it looks flipped.

Top row: the letters. Bottom row: their images.
TrickYou can never turn an image round to match the object (unless the object is itself symmetric). So an option that is just the object turned round cannot be the image — cross it out at once.
ABCD
Example 1 · Basic
A mirror stands on the right of the figure above. Choose its correct mirror image.
Solution, step by step
  1. 1Mirror on the right: left ↔ right swap, top and bottom stay.
  2. 2In G the opening is at the top right and the short bar is on the right. In the image the opening at the top left and the short bar on the left.
  3. 3Answer C. The rest: A = the figure unchanged; B = the up-down flip (a water image); D = the figure turned through 180°.
Answer Figure C
All four options show the same letter — only its direction differs.
ABCD
BasicTry it yourself first
A mirror stands on the right of the figure above. Choose its correct mirror image.
ABCD
BasicTry it yourself first
A mirror stands on the left of the figure above. Choose its correct mirror image.
ABCD
BasicTry it yourself first
A mirror stands on the right of the figure above. Choose its correct mirror image.

Where the mirror stands

A side mirror and a top-bottom mirror

The direction of the mirror line decides whether left-right or top-bottom swap.

Look at the direction of the mirror line. It tells you what will flip:

Mirror lineWhere the mirror isWhat swapsWhat stays
Vertical line |To the right or left of the figureLeft ↔ rightTop and bottom
Horizontal line —Above or below the figureTop ↔ bottomLeft and right

Here is the same F, but now the mirror lies below it. See, now F is not reversed but shown “head down”.

F in a horizontal mirror: top and bottom swap

One thing is worth noticing: whether the mirror is to the right or to the left of the figure, the image has the same shape, only its place changes. The same is true for a mirror above or below. The options show only the image, so left or right does not affect your choice.

The three-step method for every question
1. Is the mirror line vertical or horizontal?2. Decide what swaps: left-right or top-bottom3. Pick one easily recognised part, see where it goes in the image and cross out options
TrickIn step 3 always choose a part that stands alone — the arrow that points differently, the orange triangle, or the arm of a letter that sticks out on one side. Check that it is in the new place and faces the new way. Then confirm with a second part.
ABCD
Example 2 · Standard
A horizontal mirror lies above the figure shown. Choose its correct mirror image.
Solution, step by step
  1. 1Mirror above: top ↔ bottom swap, left and right stay.
  2. 2The sequence is unchanged: LEG keeps its characters in the same places, but each one is flipped upside down.
  3. 3A good clue is L: the foot is at the bottom; in the image the foot at the top.
  4. 4Answer B. The rest: A = the figure unchanged; C = the left-right flip (side-mirror image); D = the figure turned through 180°.
Answer Figure B
In a horizontal mirror the order of letters does not change, so the word still runs the same way from left to right.
ABCD
BasicTry it yourself first
A horizontal mirror lies below the figure shown. Choose its correct mirror image.
ABCD
BasicTry it yourself first
A horizontal mirror lies above the figure shown. Choose its correct mirror image.
ABCD
StandardTry it yourself first
A horizontal mirror lies above the figure shown. Choose its correct mirror image.
2

Letters, words and numbers

Which letters change and which do not

The mirror image of one letter, a whole word and a number — with the lists of letters that change and do not change.

The image of one letter

Symmetric letters do not change

The letters that do not change in a side mirror and in a top-bottom mirror, and how to read the ones that do.

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The image of a word

The order reverses and each letter flips

The two changes of a word in a side mirror (order and letters) and the one change in a horizontal mirror.

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Numbers and mixed letters and digits

Digits flip just like letters

The images of digits, the digits that do not change and mixed rows such as R5L.

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3

Figures — arrows, triangles, lines

Every part does two things: changes place and flips

The image of a figure with many parts and ways of cutting options.

How the parts of a figure change

Swap of place + flip of direction

The rules for flipping arrows, triangles and lines.

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Ways of cutting options

A landmark part, the column rule and common traps

Which option to cut first in a picture question, and the four common wrong options.

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4

The image of a clock

The hands swap sides; the time rule 11:60 − T

The hands of a clock in a mirror, the time you read and the 11:60 rule.

Clock hands in a mirror

1↔11, 2↔10, 3↔9, 4↔8, 5↔7

How to draw the image of a clock: the new place of every hand.

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The time rule: 11:60 − T

Questions without a picture

The rule for the time seen in a mirror and for the actual time.

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5

Strategy guide

The order of checks and the slips to avoid

What to look at first in any mirror question, common traps and time-savers.

The order of checks

First recognise the type

A straight order to follow in every type of question.

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Common traps and time-savers

The mistakes that keep happening

The commonest reasons for losing marks in mirror questions.

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6

Mixed practice

All types mixed

Questions of different types in three levels.

Basic practice

One letter, one part, a plain clock

Simple letters, small figures and clocks showing round times.

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Standard practice

Words, mixed rows, figures with several parts

Words, mixed rows, clocks and larger figures.

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Advanced practice

Longer words, dense figures, a mirror in any direction

Four-letter words, figures of five parts and awkward clocks.

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7

Revision — cards

Flip each card and test yourself

Think of the answer yourself first, then flip.

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