---
title: "Reflect object about y=x+1"
subject: "Computer Graphics"
chapter: 3
key: "semester_5/computer_graphics:reflect-object-y-x-plus-1"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/reflect-object-y-x-plus-1
site: BCT Engineering
---

# Reflect object about y=x+1

Computer Graphics · Chapter 3: Two –Dimensional Transformations

- Asked in: 2082 Kartik (new course), 4 marks
- Video: [Reflection about a line in Computer Graphics // numerical on reflection about a given line](https://www.youtube.com/watch?v=T3ewDqW0qjs) — Yachana Bhawsar
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/reflect-object-y-x-plus-1
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-3

## Question

Reflect the object (2, 3), (4, 3), (4, 5) about the line y = x + 1.

## Short answer

Reflection about y = x + 1 yields x' = y − 1, y' = x + 1. Point (2,3) lies on line, remains (2,3). (4,3) becomes (2,5); (4,5) remains (4,5). Reflected points: (2,3), (2,5), (4,5).

## Answer

The line y = x + 1 has m = 1 and c = 1.

```text
M = T(0,1) · R(45°) · Ref_x · R(−45°) · T(0,−1)

              | 1−m²   2m   −2mc |   | 0 1 −1 |
 M = 1/(1+m²) | 2m   m²−1    2c  | = | 1 0  1 |
              |  0     0   1+m²  |   | 0 0  1 |
```
So x' = y − 1, y' = x + 1.

```text
(2,3):  x' = 3 − 1 = 2,  y' = 2 + 1 = 3      -> (2,3)   (lies on the line)
(4,3):  x' = 3 − 1 = 2,  y' = 4 + 1 = 5      -> (2,5)
(4,5):  x' = 5 − 1 = 4,  y' = 4 + 1 = 5      -> (4,5)   (lies on the line)
```

**Answer: the reflected points are (2,3), (2,5), (4,5).**

## Check yourself

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

1. For y = x + 1, what are x' and y'?
   A. x' = y + 1, y' = x - 1
   B. x' = y - 1, y' = x + 1
   C. x' = y, y' = x
   D. x' = -y + 1, y' = -x - 1
   Answer: B. Using the general formula with m = 1, c = 1. (Key point: Mapping)

2. What happens to (2,3), which lies on y = x + 1?
   A. It moves to (3,2)
   B. It moves to (-2,-3)
   C. It stays at (2,3)
   D. It moves to (2,5)
   Answer: C. Points on the mirror line are unchanged. (Key point: Points on the line)

3. What is the image of (4,3)?
   A. (3, 4)
   B. (4, 5)
   C. (2, 3)
   D. (2, 5)
   Answer: D. x' = 3-1 = 2 and y' = 4+1 = 5. (Key point: Result)

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