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Step 1:I'll solve this step by step with precise mathematical notation:
Step 2:: Understanding Reflection
A reflection across a vertical line (in this case, $$x = -2$$) means every point is transformed by:
- Keeping the vertical (y) coordinate exactly the same - Changing the horizontal (x) coordinate by an equal distance from the line of reflection
Step 3:: Reflection Transformation Rule
- y-coordinate remains $$b
- New x-coordinate: - 2 - (a - (- 2)) = - 2 - (a + 2) = - 2 - a - 2 = - 4 - a
Step 4:: Example Demonstration
- Reflected point: $$(-7, 5)
- Original point: (3, 5)
Final Answer
x = - 2 while maintaining its vertical position.
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