The above figure shows:
A. Reflection of object about x axis.
B. Reflection of object about y axis.
C. Reflection of object about x = 0.
D. Reflection of object about y = 0.
Choose the correct answer from the options given below:

Correct option is C

The figure shows the object changing from the left side of the y-axis to the corresponding position on the right side, while its vertical coordinates remain unchanged. This is the characteristic of a reflection about the y-axis. In coordinate geometry, the y-axis is represented by x = 0, so reflection about the y-axis is also described as reflection about the line x = 0.
Under this transformation, a point (x, y) becomes (−x, y), meaning the x-coordinate changes its sign while the y-coordinate remains the same. Therefore, the figure represents reflection about the y-axis and x = 0.
Information Booster
1. Reflection about the y-axis
· The transformation is:
(x, y) → (−x, y)
· The x-coordinate changes sign, while the y-coordinate remains unchanged.
· A point at distance dd to the left of the y-axis appears at the same distance dd to its right.
· The orientation of the object is reversed.
2. Equation of the y-axis
· The y-axis is represented by: x = 0
· Therefore:
Reflection about y-axis = Reflection about x = 0
· Hence, statements B and C describe the same transformation.
3. Homogeneous transformation matrix
· Reflection about the y-axis can be represented as:
​$$\begin{bmatrix} -1&0&0\\ 0&1&0\\ 0&0&1 \end{bmatrix}$$​​
· Applying this matrix changes (x, y) into (−x, y).
4. Reflection about the x-axis
· The transformation for reflection about the x-axis is:
(x, y) → (x, −y)
· Here, the y-coordinate changes sign, unlike the transformation shown in the figure.
5. Equation of the x-axis
· The x-axis is represented by: y = 0
· Therefore, reflection about the x-axis is equivalent to reflection about y = 0.
Additional Knowledge
· Statement A — Incorrect: Reflection about the x-axis would move the object from one side of the x-axis to the other while keeping its x-coordinates unchanged. The figure instead shows a left-to-right transformation across the y-axis.
· Statement B — Correct: The object is reflected about the y-axis.
· Statement C — Correct: Since the y-axis has the equation x = 0, reflection about the y-axis is exactly reflection about x = 0.
· Statement D — Incorrect: y = 0 represents the x-axis, not the y-axis. Reflection about y = 0 would therefore be reflection about the x-axis.