---
title: "Rotate line about Y-axis by 90°"
subject: "Computer Graphics"
chapter: 4
key: "semester_5/computer_graphics:rotate-line-y-axis-90"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/rotate-line-y-axis-90
site: BCT Engineering
---

# Rotate line about Y-axis by 90°

Computer Graphics · Chapter 4: Three-Dimensional Graphics

- Asked in: 2071 Shrawan, 6 marks
- Video: [3D Rotation | CG | Computer Graphics | Lec-28 | Bhanu Priya](https://www.youtube.com/watch?v=MjUt6f_OWXg) — Education 4u
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/rotate-line-y-axis-90
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-4

## Question

Perform rotation of a line (10, 10, 10), (20, 20, 15) about Y-axis in clock wise direction by 90 degree.

## Short answer

Clockwise 90° about y-axis: x' = −z, y' = y, z' = x. P1(10,10,10) → (−10,10,10), P2(20,20,15) → (−15,20,20). The rotated line goes from (−10,10,10) to (−15,20,20).

## Answer

Rotation about the y-axis by angle θ (counter-clockwise positive, viewed from +y towards the origin):

x' = x cosθ + z sinθ, y' = y, z' = −x sinθ + z cosθ

Clockwise by 90° means θ = −90°, so cosθ = 0 and sinθ = −1:

```text
| x' |   |  0 0 -1 0 | | x |
| y' | = |  0 1  0 0 | | y |
| z' |   |  1 0  0 0 | | z |
| 1  |   |  0 0  0 1 | | 1 |
```

so x' = −z, y' = y, z' = x.

| Point | x' = −z | y' = y | z' = x | Result |
|---|---|---|---|---|
| P1(10,10,10) | −10 | 10 | 10 | (−10, 10, 10) |
| P2(20,20,15) | −15 | 20 | 20 | (−15, 20, 20) |

**Answer:** the line becomes (−10, 10, 10) to (−15, 20, 20).

## Check yourself

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

1. Clockwise rotation by 90° about y uses which angle in the standard formula?
   A. θ = -90°
   B. θ = +90°
   C. θ = 180°
   D. θ = 0°
   Answer: A. Clockwise is the negative of the standard counter-clockwise direction, so θ = -90°. (Key point: Clockwise angle)

2. With cosθ = 0 and sinθ = -1, the equations are:
   A. x' = z, y' = y, z' = -x
   B. x' = -z, y' = y, z' = x
   C. x' = -x, y' = y, z' = -z
   D. x' = y, y' = -x, z' = z
   Answer: B. x' = x cosθ + z sinθ = -z and z' = -x sinθ + z cosθ = x. (Key point: Resulting equations)

3. P1(10,10,10) goes to:
   A. (10, 10, -10)
   B. (10, -10, 10)
   C. (-10, 10, 10)
   D. (-10, -10, 10)
   Answer: C. x' = -10, y' = 10, z' = 10. (Key point: Result)

## Related in Computer Graphics

- [3D rotation about axis (1,2,3)-(10,20,30)](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Arotate-3d-axis-1-2-3) — Computer Graphics, chapter 4
- [Rotate unit cube 90° about axis AB](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Acube-rotate-90-axis-a-b) — Computer Graphics, chapter 4, asked 2×
- [Bresenham: line (10,20) to (15,2)](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Adigitize-line-10-20-15-2) — Computer Graphics, chapter 2, asked 4×
- [Bresenham: line (25,20) to (15,10)](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Adigitize-line-25-20-15-10) — Computer Graphics, chapter 2
- [Rotate object about axis y=4](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Arotate-object-about-y-4) — Computer Graphics, chapter 4
- [3D rotation about arbitrary axis](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Arotate-3d-arbitrary-axis-steps) — Computer Graphics, chapter 4, asked 2×

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