Rotation and Reflection of Figures: Rotating a Figure, Embedded Turn and Direction Changes with Rules for SSC Non-Verbal Reasoning

Many non-verbal reasoning questions need you to rotate or reflect a figure mentally. This guide on rotation and reflection of figures for SSC gives the simple rules for the rotation by 90°, 180° and 270°, how to find the new direction of an arrow or a shaded part, how letters and digits change after the rotation and the reflection, with solved examples, practice questions and FAQs. For mirror and water images, see the Mirror and Water Image note.

Rotation Basics

• Rotation turns the whole figure around its centre; the shape and size stay the same.
• Clockwise (CW) is the direction of the clock hands; anticlockwise (ACW) is the opposite.
• A full turn is 360°; a quarter turn is 90°; a half turn is 180°.
• A 90° clockwise rotation is the same as a 270° anticlockwise rotation.
• A 180° rotation looks the same clockwise and anticlockwise.

Direction Changes with Rotation

Clock Positions

A clock hand that points to 12 after a 90° CW rotation points to 3; after 180° to 6; after 270° to 9. Each hour mark is 30°, so a 45° rotation is 1.5 hours. A shaded part in the top-left corner moves to the top-right after 90° CW, the bottom-right after 180° and the bottom-left after 270° CW.

Rotation of Letters and Digits

Rotation versus Reflection

• In a vertical mirror (placed at the side), the left and right are exchanged but the top and bottom stay the same.
• In a horizontal mirror (water image: placed at the top or the bottom), the top and bottom are exchanged but the left and right stay the same.

Solved Examples

Example 1. An arrow points up. After a 90° clockwise rotation, in which direction does it point?
Right (East).

Example 2. An arrow points to the right. After a 270° clockwise rotation, in which direction does it point?
Right → (90°) Down → (180°) Left → (270°) Up.

Example 3. The shaded portion of a square is in the top-left corner. Where is it after a 180° rotation?
In the bottom-right corner.

Example 4. What does the number 69 look like after a 180° rotation?
The digits swap places and each turns: 6 becomes 9, 9 becomes 6, and the order reverses: 69 again.

Example 5. If the hour hand points to 12, where will it point after a 135° anticlockwise rotation?
135/30 = 4.5 hours back from 12: 7:30.

Example 6. If North becomes East after a rotation, what does South become?
The rotation is 90° clockwise: South becomes West.

Tips and Tricks

• Mark one reference point on the figure (for example the shaded part or an arrow tip) and track only that.
• Convert the angle into a number of quarter turns: 90° = 1, 180° = 2, 270° = 3.
• Use the clock method for the direction and the angle of the hands.
• Remember that rotation does not change the order of the parts; mirror reflection reverses it.
• Check the symmetric letters (H, I, O, X) which look the same after the 180° rotation.

Quick Tips

• Track one reference point.
• Count the quarter turns.
• Use the clock method for the directions.
• Remember that rotation preserves the order but reflection reverses it.

Quick Revision Points

• 90° CW: Up becomes Right.
• 180°: Up becomes Down.
• 270° CW is 90° ACW.
• In a vertical mirror, the left and right are exchanged.
• In 180° rotation, 6 and 9 swap.

Practice Questions With Answers

1. An arrow points left. After 90° clockwise, where does it point?
   Answer: Up
2. An arrow points down. After 180°, where does it point?
   Answer: Up
3. North becomes West after a rotation. What is the rotation?
   Answer: 90° anticlockwise
4. The shaded part is in the top-right. Where is it after 90° clockwise?
   Answer: Bottom-right
5. Which letters look the same after a 180° rotation: H, A, N, E?
   Answer: H and N
6. What does the letter b become after the 180° rotation?
   Answer: q
7. What is 90° clockwise equal to in the anticlockwise direction?
   Answer: 270° anticlockwise
8. How many hours does a 90° rotation of a clock hand cover?
   Answer: 3 hours
9. What is the difference between rotation and reflection?
   Answer: Rotation preserves the order of parts; reflection reverses it
10. An arrow points to North-East. After 90° clockwise, it points to?
    Answer: South-East

How to Practise This Chapter

Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Non Verbal Reasoning notes page, read the previous topic Pattern Completion and Incomplete Figures.

Frequently Asked Questions

What is rotation of a figure?

Turning the figure around its centre without changing its shape.

What is clockwise rotation?

Turning in the direction of the hands of a clock.

What is a 90° clockwise rotation of an arrow pointing up?

It points to the right.

How is the 270° clockwise rotation related to the anticlockwise rotation?

It equals a 90° anticlockwise rotation.

What is a reflection?

A flip of the figure over a line, like in a mirror.

What is the difference between a vertical and a horizontal mirror?

A vertical mirror swaps left and right; a horizontal mirror swaps top and bottom.

What happens to 6 and 9 after a 180° rotation?

6 becomes 9 and 9 becomes 6.

Is this topic asked in SSC?

Yes. Rotation and reflection questions appear in the SSC non-verbal reasoning section.

How much time should I take?

About 20 to 30 seconds.

How can I track the rotation easily?

Mark one reference point and follow it.

What is a quarter turn?

A rotation of 90 degrees.

What is a symmetrical letter?

A letter that looks the same after a reflection or a rotation, such as H or O.