---
title: "Scale triangle Sx=3, Sy=2"
subject: "Computer Graphics"
chapter: 3
key: "semester_5/computer_graphics:scaling-triangle-sx3-sy2"
source: https://www.bctengineer.com/q/semester_5/computer_graphics/scaling-triangle-sx3-sy2
site: BCT Engineering
---

# Scale triangle Sx=3, Sy=2

Computer Graphics · Chapter 3: Two –Dimensional Transformations

- Asked in: 2068 Bhadra (old course), 10 marks
- Video: [|| SCALING OF TRIANGLE || USING MATRICES](https://www.youtube.com/watch?v=IptcRffC9oo) — Let's Start Solving
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/computer_graphics/scaling-triangle-sx3-sy2
- Whole chapter: https://www.bctengineer.com/md/semester_5/computer_graphics/chapter-3

## Question

Perform scaling transformation to the triangle with vertices A (6, 9), B (10, 5), C (4, 3) with scaling factors Sx = 3 and Sy = 2. [Show the necessary transformation matrix]

## Short answer

Multiply each vertex by scaling factors: x' = 3x, y' = 2y. A(18,18), B(30,10), C(12,6).

## Answer

Scaling about the origin multiplies each coordinate: x' = Sx·x, y' = Sy·y.

**Scaling matrix (homogeneous):** with Sx = 3, Sy = 2

```text
S = | 3 0 0 |
    | 0 2 0 |
    | 0 0 1 |
```

The vertices as columns of the matrix P, and P' = S · P:

```text
      A   B   C                  A'  B'  C'
P = |  6  10   4 |        P' = | 18  30  12 |
    |  9   5   3 |             | 18  10   6 |
    |  1   1   1 |             |  1   1   1 |
```

Step by step:

```text
A(6,9):   x' = 3×6  = 18,   y' = 2×9 = 18
B(10,5):  x' = 3×10 = 30,   y' = 2×5 = 10
C(4,3):   x' = 3×4  = 12,   y' = 2×3 = 6
```

**Answer: A'(18, 18), B'(30, 10), C'(12, 6).** The triangle is enlarged 3 times in x and 2 times in y, and since scaling is about the origin, it also moves away from the origin.

## Check yourself

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

1. Which matrix does Sx = 3, Sy = 2 give?
   A. diag(3, 2, 1)
   B. diag(2, 3, 1)
   C. [[1,0,3],[0,1,2],[0,0,1]]
   D. diag(3, 2, 0)
   Answer: A. Scaling puts the factors on the diagonal. (Key point: Scaling matrix)

2. What is A' for A(6,9)?
   A. (9, 11)
   B. (18, 18)
   C. (12, 27)
   D. (18, 11)
   Answer: B. 3*6 = 18, 2*9 = 18. (Key point: Apply)

3. What is B' for B(10,5)?
   A. (13, 7)
   B. (20, 15)
   C. (30, 10)
   D. (30, 5)
   Answer: C. 3*10 = 30, 2*5 = 10. (Key point: Apply 2)

4. Why does the triangle also move?
   A. Translation is included
   B. Rotation is included
   C. The matrix has a translation part
   D. Scaling is about the origin so points move away from it
   Answer: D. Points are multiplied relative to the origin. (Key point: Effect)

## Related in Computer Graphics

- [Scaling about arbitrary fixed point](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Ascaling-about-fixed-point) — Computer Graphics, chapter 3
- [Triangle window to viewport mapping](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Aviewing-transform-triangle-window-viewport) — Computer Graphics, chapter 3
- [Reflect triangle about y=x+2](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Areflect-triangle-y-x-plus-2) — Computer Graphics, chapter 3
- [3D scaling about arbitrary point](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Ascale-3d-arbitrary-point) — Computer Graphics, chapter 4
- [3D window to viewport transformation](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Awindow-viewport-3d-matrix) — Computer Graphics, chapter 4
- [3D shearing and matrix](https://www.bctengineer.com/question.md?key=semester_5%2Fcomputer_graphics%3Awhat-is-3d-shearing) — Computer Graphics, chapter 4, asked 3×

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