In coordinate geometry, what are the coordinates of the reflection of the point (2, 5) in the x axis?

Introduction / Context:
This question is about reflections in coordinate geometry. Reflecting a point in the x axis or y axis is a common transformation tested in school mathematics and various aptitude exams. Understanding how coordinates change under such transformations is important for geometry and graph based questions.

Given Data / Assumptions:

• Original point is (2, 5)
• We reflect this point in the x axis.
• The coordinate plane follows the standard convention: x horizontal, y vertical.

Concept / Approach:
Reflection in the x axis keeps the x coordinate the same and reverses the sign of the y coordinate. In general:

• Reflection of (x, y) in x axis is (x, -y)
• Reflection of (x, y) in y axis is (-x, y)

We apply the first rule to the given point (2, 5).

Step-by-Step Solution:
Original point is (2, 5) For reflection in x axis, x stays same and y changes sign Keep x = 2 Change y from 5 to -5 Reflected point is (2, -5)

Verification / Alternative check:
Visually, the x axis is the horizontal line y = 0. The point (2, 5) lies 5 units above this axis. Reflection places the point 5 units below the axis at (2, -5). The x coordinate remains 2 because the point is directly above and below the same vertical line.

Why Other Options Are Wrong:
Option a, (2, 5), is the original point and not its reflection. Option b, (-2, 5), corresponds to reflection in the y axis. Option d, (-2, -5), would be obtained by reflecting in both axes. Option e, (-5, 2), does not follow any standard reflection of (2, 5) in a coordinate axis.

Common Pitfalls:
A common mistake is to swap coordinates instead of changing the sign of one coordinate. Another error is to change the sign of the wrong coordinate, for example writing (-2, 5) for reflection in the x axis. Remember that reflection in the x axis affects the vertical position, which is controlled by the y coordinate.

Final Answer:
The reflection of (2, 5) in the x axis is (2, -5).