Non Verbal Reasoning : Shape Rotations and Reflections (Type 3)

The Shape Rotations and Reflections question type requires you to work out which of the answer options, when either rotated or reflected, would bring you back to the original shape.

You will be told which of the two you need to do, so for example, on the question sheet you will be instructed to either rotate or reflect the shape.

The original shape would be on the left hand side of a vertical line / separator. On the right hand side you will be given 4 or 5 different options. These options have not been rotated or reflect, that is what you have to do.

There is only one answer which would bring you back to the original shape, the other 4 options would not get you to the original shape. You are allowed to rotate or reflect, depending on the instructions, your option as many times as you want.

Just in case these are new terms to you, here is a quick table with a few definitions, including an additional one which is flip that is very similar to reflection:

With this question type there are no rules, characteristics or patterns you have to establish, something you would have to do in non-verbal reasoning questions such as Odd One Out.

Instead, this is pure shape transformation and shape shifting. You are expected to be able to manipulate and change the answer option based on the instruction given to you to find which of the answers gets you back to the original shape – and do it in the most efficient way possible.

The way you work this out is totally up to you, whether you do it visually on paper or in your mind, but what is most important here is to make sure you are practising your ability to change and transform shapes from a start position to an end position. What this will do is prepare your mind to logically understand how things should look when transformed into a new position.

Now although this is pure shape transformation you will come across questions with normal and abnormal shapes which is where things can become difficult. These can include simple shapes, complex shapes, multiple shapes overlapped or merged together, pattern-based shapes as well as a combination of all these things.

Now in order to stop yourself from getting confused and having a robust process in place, it is important to first recognise that this question type is testing the following core skills:

• Ability to identify and note qualities of the main shape
• Ability to determine which of the answer options meet the qualities present before and after transformation
• Ability to move and rearrange shapes in different directions
• Ability to rotate shapes clockwise and anti-clockwise e.g. 45deg, 90deg, 135deg and 180deg
• Ability to track specific changes to different parts of the shape whilst it is being transformed
• To be able to review specific details when differentiating between potential answers
• Knowing how to take a shape from a start position to an specific end position
• Able to read instructions clearly
• Ability to put aside answer options that do not follow the logic of the instruction e.g. answers which are mirrored but the question asks you to rotate

Other than the wider skills around time management, logic and a step by step though process it is clear a question type like this focuses purely on your shape transformation skills, and where you have shapes which look the same, taking a detailed look at the different elements that make up that shape.

What this means is that you are able to look at a set of shapes and manipulate / change them in a specific way to identify which one will get you back to the original shape – after doing this you can then select your answer.

How does the Shape Rotations and Reflections Question Type Look Like?

As you can see from the Gaggle example below, the Shape Rotations and Reflections question type is in the following format:

• Instructions with an example of an answered question
• Set of questions
• Original transformation on the left of a vertical line
• 4 to 5 options on the right of the vertical line which is where you select your answer from based on which shape you think can be transformed back to the original shape
• 1 mark per question

How do I answer this question?

In order to be able to rotate and / or reflect correctly it really is one main thing. That is understanding how to transform shapes from a start position to an end position. The instructions for the question will be and are clear as you can see from the reflection example above.

REMEMBER : The answer options have not been reflected or rotated, you need to do that either in your head or on paper to see which one gets you back to the original shape

It is up to you to select the answer from the options given to you which, when reflected or rotated, gets you back to the original position. It is vital you practice so that you become both familiar and comfortable with changing shapes.

As you progress, and get more complex questions there will be more things to consider, for example:

1. The order and position of multiple shapes once changed
2. The look and positioning of colours and patterns
3. How edges, curves and corners are once transformed

But as you can tell, it all boils down to your ability to move a shape whilst keeping everything consistent with its original space or area. Like with all other question types, in order to do this accurately you need to have an idea of an approach or process. So lets break that down:

1. Take information in visually and read the instructions – what is it asking you to do?
2. Look at the original shape and study all its elements incl. the inner shapes / colours and patterns
3. Build out a list of qualities to refer back to
4. Look at all the potential answer options
5. Start with Shape A, and based on the instruction to reflect or rotate, apply the process – ask the question, does it get you back to the original shape?
6. Map and track the different elements so that they are consistent / still in their right positions or places
7. If it doesn’t move on to the next shape
8. Double check

What it means to rotate

Rotation is one form of shape transformation. To rotate a shape all you need to do is pick out its center, and then spin the full shape around that center. You can spin it clockwise or anti-clockwise, but it is important that when you spin it, the whole shape moves.

There is no need to move it right or left or up and down, because with rotation, all it needs to do is spin around the center. There are some standard degrees that a shape can be expected to spin these are : 45deg, 90deg, 135deg, 180deg, 225deg, 270deg, 315deg, 360deg

Always remember, spin the shape as much as you need to, to confirm whether it will return back to the original shape.

What it means to reflect

Reflection is another form of shape transformation and the best way to understand it is to imagine a mirror. When anything is put in front of a mirror the image is reversed or flipped and that is what you want to do here. You can reverse the image or shape from top, bottom, left and right, but it is important to remember here that when you reflect something the position of things like corners etc. always goes to the opposite.

So for example if you reflect a shape from the side, what was on the left will now be on the right.

And if you reflect it from the top, what was on the bottom will now be on the top. There are 3 variations of reflections you can have which means you may need more than one step in your working out process:

• Immediate reflection on either side e.g. left to right and right to left
• Immediate reflection on the top or bottom
• Reflection which occurs with both side and top and bottom

Working Example

Question 1

Now that we have a process in place, and we understand what it means to rotate and / or reflect, lets apply the process to the Working Example.

In the Working Example Question 1 we can see clearly that it is asking us to Reflect as the word Reflect is above the vertical seperator.

Looking at the original shape on the left side of the seperator we can see that it is an arrow with the following qualities:

1. It has a black border with no inner colour
2. It is pointing to the left
3. There is a smaller triangle inside which also has a black border with an inner grey colour
4. The top of the small triangle also points to the top of the arrow

Now that we have done this we know what qualities the answer options need to have to be a potential answer.

Lets start looking through our answer options – keeping in mind we need to reflect or flip this shape to get back to our main shape.

First of all, all our answer options tick off qualities 1 and 3 of the original shape they all are an arrow with a border and have a smaller grey, bordered triangle inside them.

Now, because we know this we can move on quickly to see which shape meets qualities 2 and 4.

Lets start with Shape A, it is pointing down, if we flipped this it would point up, so this cannot be the answer as our main answer option is pointing to the left.

Shape B is pointing to the right, if we flipped this it would point to the left – that is exactly the same direction our main shape is pointing in BUT, there is one more quality we need to match which is the smaller triangle.

The top of the triangle needs to point to the top of the arrow, but in Shape B the top of the triangle is pointing to the bottom of the arrow so this cannot be our answer.

Lets look at Shape C, it is also facing right, which if we reflect will then face left, just like our main shape.

Looking at the smaller triangle we can see the top of the triangle is pointing towards the top of the arrow – so from there we can understand that if we flipped Shape C we would get back to our main shape position.

So our answer must be Shape C.

Shape D cannot be an answer only because it is already pointing left, if we were to reflect it, it would point right so it would not return us back to the original shape.

What if I can’t work out the changes?

It is important to understand how much practice you need to do in order to get to a position where you can quickly do this in your head. There is a lot of visual information given to you to first absorb and then change / transform. This is not an easy task to do – and as shapes get more complex with more elements it can become difficult.

In the situation where you are beginning to struggle, always try to take a step back and give yourself time to think. Where you cannot work out the answer in a few attempts, try the following:

• Using your list of qualities eliminate any of the answer options which do not meet the quality for example, if your main shape is pointing left, but your answer option is pointing down, you know that if you were to reflect it, it would never face left, so you can eliminate that option
• Break down the shapes to their individual parts
• Take a step by step approach, looking at each thing one by one
• Make sure you are rational, something that is pointing down will never point left when reflected or flipped
• Rotate and reflect on paper, draw it out on paper if you need to
• Look at one shape at a time
• Remember you need to find the shape, which when transformed, gets you back to the original shape on the left
• A answer option that you are going to reflect will not have elements that are already facing in the same direction as the original shape for example if your arrow is pointing to the right in your original shape, then your answer option cannot also be pointing right because thats not what its meant to look like before being reflected