Aspire Faculty ID #19246 · Topic: UGC NET Computer Science June 2019 (Paper II) · Just now
UGC NET Computer Science June 2019 (Paper II)

Consider the following statements regarding $2D$ transforms in computer graphics:

$S1$: [
1 0
0 -1
]
is a $2 \times 2$ matrix that reflects any $2D$ point about the $X$-axis.

$S2$: A $2 \times 2$ matrix which mirrors any $2D$ point about the $X$-axis, is a rotation matrix.

What can you say about the statements $S1$ and $S2$?

Solution

Given matrix is

[
1 0
0 -1
]

When this matrix is applied on point $(x,y)$, then the point becomes $(x,-y)$.

This means the sign of $x$ remains same and the sign of $y$ changes.

So, this represents reflection about the $X$-axis.

Therefore, statement $S1$ is true.

But reflection about the $X$-axis is not a rotation matrix.

Therefore, statement $S2$ is false.

Hence, the correct answer is Option 2.

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