AExE02 · Chapter 2Theory of Computation & Graphics🏛️ Past Licensure QuestionID: f35620e3

What 2D transformation is represented by the following homogeneous coordinate diagonal matrix:
$\begin{bmatrix} s_x & 0 & 0 \\ 0 & s_y & 0 \\ 0 & 0 & 1 \end{bmatrix}$
?

Multiple Choice Options

A
Rotation
B
Scaling
✓ Correct Option
C
Translation
D
Shearing

Detailed Technical Solution & Explanation

Multiplying a 2D coordinate vector $\begin{bmatrix} x & y & 1 \end{bmatrix}^T$ by this matrix yields $x' = s_x \cdot x$ and $y' = s_y \cdot y$ , which is the standard affine matrix representation of Scaling.

Option Analysis:

•

Option A (Rotation): Contains trigonometric sine and cosine elements.

•

Option B (Scaling): Correct. Diagonal matrix containing scaling factors

s_x

and

s_y

•

Option C (Translation): Contains translation offsets in the third column

\begin{bmatrix} 1 & 0 & t_x \\ 0 & 1 & t_y \\ 0 & 0 & 1 \end{bmatrix}

•

Option D (Shearing): Contains shear factors in the off-diagonal positions.

Reference: Demo2 · Set 2NEC Licensure Syllabus

What 2D transformation is represented by the following homogeneous coordinate diagonal matrix:
$\begin{bmatrix} s_x & 0 & 0 \\ 0 & s_y & 0 \\ 0 & 0 & 1 \end{bmatrix}$
?

Multiple Choice Options

Detailed Technical Solution & Explanation

Option Analysis:

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What 2D transformation is represented by the following homogeneous coordinate diagonal matrix:
$\begin{bmatrix} s_x & 0 & 0 \\ 0 & s_y & 0 \\ 0 & 0 & 1 \end{bmatrix}$
?

Multiple Choice Options

Detailed Technical Solution & Explanation

Option Analysis:

Want to practice this topic interactively?