What are the coordinates of the reflection of the point (-0.5, 6) in the x-axis?

Introduction / Context:
This question tests understanding of reflections of points across the coordinate axes in the Cartesian plane. Reflecting a point across the x-axis changes its vertical position while keeping the horizontal coordinate the same. Recognising how the sign of the y coordinate changes under such a reflection is the key idea here.

Given Data / Assumptions:

• Original point is P(-0.5, 6).
• Reflection is to be taken in the x-axis.
• In Cartesian coordinates, x-axis reflection flips the sign of the y coordinate but leaves the x coordinate unchanged.

Concept / Approach:
When a point (x, y) is reflected across the x-axis, its image becomes (x, -y). The x coordinate remains the same because the point stays directly above or below its original horizontal position. The y coordinate changes sign because the point moves to the opposite side of the x-axis by the same vertical distance. Applying this rule to the given point yields the answer directly.

Step-by-Step Solution:
Given point P has coordinates (-0.5, 6).Reflection in x-axis sends (x, y) to (x, -y).Here x = -0.5 and y = 6.So the reflected point P' has coordinates (x, -y) = (-0.5, -6).Therefore the reflection of (-0.5, 6) in the x-axis is (-0.5, -6).

Verification / Alternative check:
Visually, the original point is 0.5 units to the left of the origin and 6 units above the x-axis. Its reflection across the x-axis should be directly below at the same horizontal position, that is 6 units below the x-axis. This gives coordinates (-0.5, -6), matching our algebraic result. This geometric reasoning confirms the correctness of the answer.

Why Other Options Are Wrong:
(0.5, -6) changes both coordinates, which corresponds to a reflection across the origin combined with a horizontal flip, not just across the x-axis. (-6, -0.5) and (6, -0.5) swap the roles of x and y, which would be a reflection across the line y = x or similar, not across the x-axis. (-0.5, 6) is the original point and shows no reflection at all. Only (-0.5, -6) correctly applies the rule (x, y) to (x, -y).

Common Pitfalls:
Students often confuse reflection across the x-axis with reflection across the y-axis. Reflection across the y-axis would change (x, y) to (-x, y). It is useful to remember that x-axis reflection flips the sign of y, and y-axis reflection flips the sign of x. Careful reading of the axis name and the coordinates helps avoid such mix ups.

Final Answer:
(-0.5, -6)