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In coordinate geometry, find the reflection image of the point (-1, 5) in the vertical line x = 1. What are the coordinates of the reflected point?

Difficulty: Easy

Correct Answer: (3, 5)

Explanation:


Introduction / Context:
This question tests reflection of a point across a vertical line in the Cartesian plane. A reflection across x = a keeps the y-coordinate unchanged and shifts the x-coordinate symmetrically across the line.


Given Data / Assumptions:

  • Original point: P(-1, 5)
  • Mirror line: x = 1
  • Reflection is perpendicular to the mirror line.


Concept / Approach:
For reflection across x = a: x' = 2a - x y' = y This works because the mirror line lies exactly midway between the original point and its image along the horizontal direction.


Step-by-Step Solution:

Here the mirror line is x = 1, so a = 1. Original x-coordinate is x = -1. Compute reflected x: x' = 2*1 - (-1) = 2 + 1 = 3. The y-coordinate does not change for a vertical reflection: y' = 5. So the reflected point is (3, 5).


Verification / Alternative check:
The midpoint of (-1, 5) and (3, 5) is ((-1+3)/2, (5+5)/2) = (1, 5). The midpoint lies on x = 1, confirming a correct reflection.


Why Other Options Are Wrong:

(-3, 5) reflects across x = -2, not x = 1. (1, 5) is on the mirror line, not the reflected image. (3, -5) wrongly changes the y-coordinate (that would happen for reflection across the x-axis). (-1, 5) is the original point, meaning no reflection was applied.


Common Pitfalls:
Changing both coordinates, or averaging incorrectly. Remember: vertical line reflection changes only x, not y.


Final Answer:
(3, 5)

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