Which is the correct representation in the options, if the image K shown below is flipped about the vertical axis (shown on the right side of K)?
Show Hint
For reflection problems, focus on an asymmetric feature. For example, the top-right element in K is a mirrored '5'. After a vertical flip, this element must become a regular '5' and move to the top-left position. This single observation immediately identifies D as the only possible answer.
Step 1: Understanding the Question:
The task is to perform a horizontal flip (reflection about a vertical axis) on the given image K and identify the correct resulting image from the options. Step 2: Key Formula or Approach:
A horizontal flip means every point on the left side of the image moves to a corresponding position on the right side, and vice-versa. It's like looking at the image in a mirror. We can analyze the transformation row by row. The order of the elements in each row will be reversed, and each element itself will be mirrored. Step 3: Detailed Explanation:
Let's analyze Image K, which is a 3x3 grid of characters based on the digits '2' and '5'. Let's denote the mirror image of a character with a 'mir-' prefix.
- Original Top Row: `[2, 2, mir-5]`
- When flipped, the order reverses to `[mir-5, 2, 2]`.
- Each character is also flipped: `[mir-(mir-5), mir-2, mir-2]` which simplifies to `[5, mir-2, mir-2]`.
- Original Middle Row: `[5, mir-5, 2]`
- Flipped order: `[2, mir-5, 5]`
- Flipped characters: `[mir-2, mir-(mir-5), mir-5]` which simplifies to `[mir-2, 5, mir-5]`.
- Original Bottom Row: `[5, 2, mir-5]`
- Flipped order: `[mir-5, 2, 5]`
- Flipped characters: `[mir-(mir-5), mir-2, mir-5]` which simplifies to `[5, mir-2, mir-5]`.
So, the resulting flipped image should be:
- Top Row: `[5, mir-2, mir-2]`
- Middle Row: `[mir-2, 5, mir-5]`
- Bottom Row: `[5, mir-2, mir-5]` Step 4: Final Answer:
Comparing this resulting grid with the options, we find that Image D is an exact match.
