Geometry

Question Analysis:
This problem combines two fundamental transformations: reflection over a vertical line followed by a translation.
The key is to apply these operations in the correct sequential order.

Key Concept Explanation:
Reflection over vertical line x = a:
Transformation rule: (x, y) → (2a - x, y)
Only the x-coordinate changes
Translation:
Rule: (x, y) → (x + h, y + k)
Left = negative x, right = positive x
Down = negative y, up = positive y

Step-by-Step Solution:
First transformation (reflection over x = 3):
Original point: (2, 4)
New x-coordinate: 2(3) - 2 = 4
Reflected point: (4, 4)
Second transformation (translation):
5 units left: x = 4 - 5 = -1
3 units down: y = 4 - 3 = 1
Final coordinates: (-1, 1)

Common Mistakes:
Applying the translation before the reflection
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