To find the coordinates of U' after a reflection across the line \( x = 1 \), we need to understand how reflections work with respect to this vertical line.
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Identify the coordinates of U: \( U = (-1, 4) \).
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Determine the distance from U to the line \( x = 1 \):
- The x-coordinate of U is -1.
- The distance from -1 to 1 is \( 1 - (-1) = 2 \).
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Reflect U across the line:
- Since you move 2 units to the right of the line \( x = 1 \), you add this distance to the x-coordinate of the line:
- \( 1 + 2 = 3 \).
Thus, the reflected coordinates of point U, U', are:
- \( U' = (3, 4) \).
However, the reflected x-coordinate isn’t present among the options given. Let's re-evaluate based on the options provided:
- Reflection transformation process:
- To reflect a point \( (x, y) \) across the line \( x = a \):
- The new x-coordinate becomes \( 2a - x \), while the y-coordinate remains the same.
With \( a = 1 \) and \( x = -1 \): \[ U' = (2 \cdot 1 - (-1), 4) = (2 + 1, 4) = (3, 4). \] This reaffirmed that U’ should be at (3, 4), which does not match any answer.
Let’s consider the provided answers and check whether any of those coordinate pairs could be perceived as U' under this reflection process, potentially indicating calculation alternatives or assumptions about reflection across y-values:
- If U = (-1, 4) and the reflection is across the vertical line x = 1, we derive U' correctly. However, results do not match choices.
Cross-verifying against provided answers:
- The coordinates have not used correct methods as there seems conflict with transformations or given points instead of the question posed.
Given the nature of problems of reflections across vertical lines and checks revealed no corresponding targets amongst chosen set of answers. From original calculation path:
- U' after reflection must read as (3, 4) indeed stands not favoring given provisions.
Please check if any constraints applied were missed or if coordinates stem from different transformations stipulated.
1 answer