In coordinate geometry, a point P has coordinates (4, −3). This point is reflected in the horizontal line y = 1. What are the coordinates of the reflected image of P after reflection in the line y = 1?

Introduction / Context:
This question checks your understanding of reflections in coordinate geometry, specifically reflection of a point in a horizontal line. Such transformations appear frequently in school level analytic geometry and in aptitude exams that test spatial reasoning.

Given Data / Assumptions:

• Original point P has coordinates (4, −3).
• Reflection line is the horizontal line y = 1.
• We need the coordinates of the reflected point P prime.

Concept / Approach:
Reflection in a horizontal line y = k keeps the x coordinate unchanged while the y coordinate is mirrored across the line. The vertical distance from the point to the line is preserved on the other side. If the original y coordinate is y1, then the reflected point has y coordinate y2 such that the midpoint of y1 and y2 is k.

Step-by-Step Solution:
The original point is P(4, −3). The reflection line is y = 1, so k = 1. For reflection across y = 1, x stays the same: x2 = 4. Let the new y coordinate be y2. The line y = 1 is exactly midway between −3 and y2. So the midpoint relation is (−3 + y2) / 2 = 1. Multiply both sides by 2: −3 + y2 = 2. Thus y2 = 2 + 3 = 5. Hence the reflected point is (4, 5).
Verification / Alternative check:
The vertical distance from −3 to 1 is 4 units. From 1 to 5 is also 4 units. Since distances are equal on both sides of the reflecting line, this confirms the reflection is correct.

Why Other Options Are Wrong:
Option a (4, −5) goes further away from the line y = 1 on the same side instead of the opposite side. Options c and d change the x coordinate sign without justification. Option e (5, 4) changes both coordinates and does not preserve the horizontal alignment with the original point.

Common Pitfalls:
A common mistake is to reflect across the wrong axis, for example treating the reflection as if it were across the x axis (y = 0) instead of y = 1. Another frequent error is to change both coordinates when reflecting in a horizontal line, even though only the y coordinate should change.

Final Answer:
The reflected image of the point (4, −3) in the line y = 1 is (4, 5).