---
title: "Short note: 2D translation"
subject: "Computer Graphics"
chapter: 3
key: "semester_5/computer_graphics:short-note-2d-translation"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/short-note-2d-translation
site: BCT Engineering
---

# Short note: 2D translation

Computer Graphics · Chapter 3: Two –Dimensional Transformations

- Asked in: 2070 Asar, 2 marks
- Video: [2D Translation in Computer Graphics 🔥 | Easy Explanation with Example](https://www.youtube.com/watch?v=KWyr-_-iWcE) — Gate Smashers
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/short-note-2d-translation
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-3

## Question

Write a short note on 2D translation.

## Short answer

Translation moves points by adding offsets: x'=x+tx, y'=y+ty. In homogeneous 3×3 matrix form. It preserves shape and size. Inverse is translation by (-tx,-ty). Two successive translations add: T(tx1,ty1)·T(tx2,ty2)=T(tx1+tx2,ty1+ty2).

## Answer

**Translation** moves an object from one position to another along a straight path without changing its shape or size. Every point P(x, y) is shifted by translation distances tx (along x) and ty (along y):

x' = x + tx, y' = y + ty

Matrix form (homogeneous coordinates):

```text
| x' |   | 1 0 tx | | x |
| y' | = | 0 1 ty | | y |
| 1  |   | 0 0 1  | | 1 |
```

Points:
- It is a rigid-body transformation: distances and angles are preserved.
- Inverse translation is T(−tx, −ty).
- Two translations add: T(tx1, ty1)·T(tx2, ty2) = T(tx1+tx2, ty1+ty2).

Example: P(2, 3) translated by (4, −1) gives P'(6, 2).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What are the translation equations?
   A. x' = x·tx, y' = y·ty
   B. x' = x - y
   C. x' = tx, y' = ty
   D. x' = x + tx, y' = y + ty
   Answer: D. Each point is shifted by tx and ty. (Key point: Equations)

2. What is the inverse of T(tx,ty)?
   A. T(-tx,-ty)
   B. T(1/tx,1/ty)
   C. T(ty,tx)
   D. R(180°)
   Answer: A. Shift back by the negatives. (Key point: Inverse)

3. P(2,3) translated by (4,-1) gives?
   A. (6, 4)
   B. (6, 2)
   C. (-2, 4)
   D. (8, -3)
   Answer: B. 2+4 = 6 and 3-1 = 2. (Key point: Example)