Water Images

What you need to understand

The water lies below the figure, so top and bottom change places.

Left and right do not change. A mark on the left of the figure stays on the left of the image.

The image is a reflection, not a rotation. Turning the figure through half a turn swaps left and right as well, and gives the wrong answer.

The water image of the water image is the original figure.

A figure that is symmetric about its horizontal centre line is its own water image.

Height is mirrored: a feature twice as high above the waterline appears twice as deep below it.

A figure standing on the waterline has a reflection meeting it along that line, which is a useful clue when checking an option.

How to work through these questions

Find the feature that sits highest in the figure, since it will move furthest.

Reflect it: keep it on the same side, and move it to the same distance below the waterline.

Work down through the figure, reflecting each feature in turn.

Eliminate the option that is the figure unchanged.

Eliminate the option that is the figure turned through half a turn, which is the commonest wrong answer.

Eliminate the mirror image, in which left and right are swapped instead of top and bottom.

Check the option that survives by reflecting a second feature and finding it in the right place.

Mistakes that cost marks

Mistaking the mirror image for the water image. In the mirror image left and right change places; in the water image top and bottom do.
Turning the figure upside down by rotating it, which also swaps left and right, instead of reflecting it.
Reflecting the outline and leaving an internal mark where it was.
Assuming a figure is symmetric about the horizontal line when it is not, so that the original looks like a valid option.
Using the wrong waterline, for instance reflecting about the bottom edge of the figure rather than its centre line.
Checking a single feature when two options differ only in another.

Worked example

A figure has a short bar across its top and a dot in its lower-left area. Which figure is its water image?

The water lies below the figure, so top and bottom change places and left and right do not.
The bar sits across the top, so in the image it sits across the bottom.
The dot sits low and on the left, so in the image it sits high and on the left.
The option with the bar at the bottom and the dot high on the left is the water image.
An option with the dot high on the right is the mirror image, not the water image.

Answer: The bar moves to the bottom and the dot to the upper-left, staying on the left.

Practice questions with answers

A few Water Images questions with the full solution shown, so you can see how the method is applied before you attempt the timed set.

Question 1

Which of the four figures is the water image of the figure shown, given that the figure is reflected in water lying below it?

Answer: Option C — with explanation

The water image is formed by reflecting it in water lying below it, which swaps its top and bottom and leaves its left and right alone. Exactly one of the four figures matches after that reflection. The other three are the figure unchanged, the figure turned through half a turn, and the mirror image. Common mistakes - gave the mirror image, which is a reflection about the other axis - turned the figure through half a turn instead of reflecting it - left the figure exactly as it was

Question 2

The figure shown is the water image of exactly one of the four figures below. Which one?

Answer: Option B — with explanation

The figure shown is a water image, so it was made by reflecting it in water lying below it, which swaps its top and bottom and leaves its left and right alone. To recover the figure it was made from, reflect it the same way a second time: reflecting twice brings a figure back to where it started. The other three options are the figure shown itself, the figure a half turn away from the answer, and the mirror image of the answer. Common mistakes - gave the reflection itself, which is the picture already on show, rather than the figure it was made from - gave the mirror image of the figure shown, which is the wrong axis - reflected the figure the wrong way round twice over, arriving a half turn away

Question 3

Which of the four figures is the water image of the figure shown, given that the figure is reflected in water lying below it?

Answer: Option A — with explanation

The water image is formed by reflecting it in water lying below it, which swaps its top and bottom and leaves its left and right alone. Exactly one of the four figures matches after that reflection. The other three are the figure unchanged, the figure turned through half a turn, and the mirror image. Common mistakes - turned the figure through half a turn instead of reflecting it - gave the mirror image, which is a reflection about the other axis - left the figure exactly as it was

Question 4

The figure below is the water image of one of these four figures. Which one?

Answer: Option B — with explanation

The figure shown is a water image, so it was made by reflecting it in water lying below it, which swaps its top and bottom and leaves its left and right alone. To recover the figure it was made from, reflect it the same way a second time: reflecting twice brings a figure back to where it started. The other three options are the figure shown itself, the figure a half turn away from the answer, and the mirror image of the answer. Common mistakes - gave the mirror image of the figure shown, which is the wrong axis - gave the reflection itself, which is the picture already on show, rather than the figure it was made from - reflected the figure the wrong way round twice over, arriving a half turn away

Question 5

Which of the four figures is the water image of the figure shown, given that the figure is reflected in water lying below it?

Answer: Option D — with explanation

The water image is formed by reflecting it in water lying below it, which swaps its top and bottom and leaves its left and right alone. Exactly one of the four figures matches after that reflection. The other three are the figure unchanged, the figure turned through half a turn, and the mirror image. Common mistakes - left the figure exactly as it was - gave the mirror image, which is a reflection about the other axis - turned the figure through half a turn instead of reflecting it

Frequently asked questions

How is a water image different from a mirror image?

A water image is a reflection about a horizontal line, so top and bottom change places. A mirror image is a reflection about a vertical line, so left and right change places instead.

Is a water image the same as turning the figure upside down?

No. Turning the figure upside down rotates it by half a turn, which changes left-right as well as top-bottom. In a water image left and right stay where they were.

Where is the waterline?

Through the centre of the figure, unless the question says otherwise. Every feature is reflected the same distance on the other side of that line.

What if the figure is symmetric about its horizontal line?

Then the figure is its own water image, and the original would be a correct answer, so the question could not have a single answer. Such figures are avoided.

Do letters and numerals behave the same way in water?

Yes. Every stroke is reflected in the same way, so a numeral standing upright appears upside down in the reflection, on the same side as before.