Image K is rotated by an angle of 45 degrees anticlockwise. Which option represents the rotated image?
Show Hint
In mental rotation tasks, instead of trying to rotate the entire complex image at once, pick one unique point or feature. Rotate only that feature to its new position and then check which of the options has that feature in the correct place. This simplifies the process and reduces errors.
Step 1: Understanding the Question:
We need to perform a mental rotation of the given image 'K' by 45 degrees in the counter-clockwise (anticlockwise) direction and identify the correct resulting image from the options. Step 2: Key Formula or Approach:
To solve this, we can focus on a specific, easily identifiable feature of the original image K and track its position after the rotation. The overall shape of the pattern in K is a square, which will appear as a diamond after a 45-degree rotation. Step 3: Detailed Explanation:
Let's observe Image K. It has a central pattern with distinct protrusions on its top, bottom, left, and right sides. Let's focus on the protrusion at the top center, which consists of a 2x1 block of filled squares.
- A 45-degree anticlockwise rotation will move this top feature to a top-left position.
- Similarly, the feature on the right side will move to the top-right.
- The feature on the bottom will move to the bottom-left.
- The feature on the left will move to the bottom-right.
Now let's examine the options:
- Option A: The top feature of K has moved to the left. This represents a 90-degree anticlockwise rotation. Thus, it is incorrect.
- Option B: The top feature of K has moved to the top-left position. The right feature has moved to the top-right. This perfectly matches a 45-degree anticlockwise rotation.
- Option C: The orientation is incorrect and does not correspond to a simple rotation of K. It appears to be a combination of rotation and reflection.
- Option D: The top feature of K has moved to the top-right. This represents a 45-degree clockwise rotation. Thus, it is incorrect. Step 4: Final Answer:
Option (B) is the only image that correctly depicts Image K after a 45-degree anticlockwise rotation.
