Mirror Images

What you need to understand

The mirror stands vertically on the right, so left and right change places.

Top and bottom do not change. A mark at the top of the figure stays at the top of the image.

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

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

A figure that is symmetric about its vertical centre line is its own mirror image, so a question using one could not have a single answer.

Distance from the mirror is what matters: a mark twice as far from the mirror line as another appears twice as far on the other side.

A numeral or letter changes shape when reflected. The mirror image of a capital F is not the letter F reversed in reading order but a new shape with its arm on the other side.

How to work through these questions

Find the most distinctive feature of the figure - a notch, a corner, a diagonal - and note where it sits, left or right of centre, and high or low.

Reflect that feature: keep its height, move it to the opposite side.

Check the rest of the figure against the same rule rather than by eye.

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 water image, in which top and bottom are swapped instead of left and right.

Confirm the option that survives by reflecting one more feature and finding it there too.

Mistakes that cost marks

Mistaking the water image for the mirror image. In the water image top and bottom change places; in the mirror image left and right do.
Mistaking a half turn for a mirror reflection. A half turn swaps both pairs of directions, a mirror reflection swaps only one.
Reflecting only the outline and leaving the internal detail as it was.
Assuming the figure is symmetric when it is not, which makes the original look like a valid answer.
Reading the option in the order the shapes appear rather than by the positions they occupy.
Checking one feature and stopping, when two options differ only in a second feature.

Worked example

A figure has a small square in its top-left corner and a sloping line running down towards the right. Which figure is its mirror image?

The mirror stands vertically on the right, so left and right change places and top and bottom do not.
The small square sits high and on the left, so in the image it sits high and on the right.
The sloping line runs down towards the right, so in the image it runs down towards the left.
The option with the square high on the right and the line sloping down to the left is the mirror image.
A figure with the square low on the right is the water image, not the mirror image, and can be discarded.

Answer: The square moves to the top-right corner and the slope runs down towards the left.

Practice questions with answers

A few Mirror 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 mirror image of the figure shown, given that a vertical mirror stands on the right-hand side of the figure?

Answer: Option D — with explanation

The mirror image is formed by reflecting it in a mirror standing on its right, which swaps its left and right and leaves its top and bottom 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 water image. Common mistakes - left the figure exactly as it was - turned the figure through half a turn instead of reflecting it - gave the water image, which is a reflection about the other axis

Question 2

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

Answer: Option B — with explanation

The figure shown is a mirror image, so it was made by reflecting it in a mirror standing on its right, which swaps its left and right and leaves its top and bottom 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 water 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 water 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 mirror image of the figure shown, given that a vertical mirror stands on the right-hand side of the figure?

Answer: Option A — with explanation

Question 4

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

Answer: Option C — with explanation

The figure shown is a mirror image, so it was made by reflecting it in a mirror standing on its right, which swaps its left and right and leaves its top and bottom 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 water image of the answer. Common mistakes - reflected the figure the wrong way round twice over, arriving a half turn away - gave the reflection itself, which is the picture already on show, rather than the figure it was made from - gave the water image of the figure shown, which is the wrong axis

Question 5

Which of the four figures is the mirror image of the figure shown, given that a vertical mirror stands on the right-hand side of the figure?

Answer: Option A — with explanation

The mirror image is formed by reflecting it in a mirror standing on its right, which swaps its left and right and leaves its top and bottom 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 water image. Common mistakes - left the figure exactly as it was - gave the water 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 mirror image different from a water image?

A mirror image is a reflection about a vertical line, so left and right change places. A water image is a reflection about a horizontal line, so top and bottom change places. The two are not the same picture.

How is a mirror image different from turning the figure through half a turn?

A half turn changes both left-right and top-bottom at once. A mirror image changes only left-right, so the two differ by a water image. If an option matches the figure rotated by 180 degrees, it is not the mirror image.

What if the figure is symmetric?

A figure symmetric about its vertical centre line coincides with its own mirror image. Such a figure cannot be used for a mirror question with one answer, because the original would be correct as well.

Do I have to reverse the order the shapes are drawn in?

No. What changes is where each shape sits, not the order they were drawn in. Move each shape to the mirrored position and leave it there.

Why does a letter look wrong rather than simply backwards?

Because the reflection acts on the whole glyph, including the direction its strokes lean. A reflected letter is a picture of the letter seen in a mirror, which is generally not another letter.