In this aptitude (simplification and coordinate geometry) question, you must find the reflection of a point across the y axis. Given the point (2, 7), determine its reflected point in the y axis, remembering that only the sign of the x coordinate changes.

Introduction / Context: This question comes from basic coordinate geometry and focuses on reflections across axes. Reflecting points is a common task when sketching graphs, analysing symmetry, and solving geometry problems. Here we are specifically asked to reflect a point across the y axis in the standard Cartesian plane.

Given Data / Assumptions: Original point: (2, 7). Reflection is taken in the y axis. We use the standard orientation where the x axis is horizontal and the y axis is vertical.

Concept / Approach: Reflection across the y axis leaves the y coordinate unchanged and reverses the sign of the x coordinate. That is, any point (x, y) becomes (-x, y) after reflection in the y axis. This arises because the y axis is the mirror line and points on it have x = 0, so distances perpendicular to the axis are preserved but taken to the opposite side.

Step-by-Step Solution: Identify the coordinates of the given point: x = 2 and y = 7. For reflection in the y axis, transform (x, y) to (-x, y). Apply this rule: (2, 7) becomes (-2, 7). Thus the reflected point has x coordinate -2 and y coordinate 7.

Verification / Alternative check: We can visualise the point on a coordinate grid. The point (2, 7) lies to the right of the y axis. Its mirror image in the y axis should lie at the same height (same y value) but the same distance on the left side of the y axis. That point is (-2, 7). This simple geometric reasoning is consistent with the algebraic rule (x, y) goes to (-x, y).

Why Other Options Are Wrong: Option (2, -7) reflects the point across the x axis, not the y axis. Option (-2, -7) is a reflection through the origin, combining reflections in both axes. Option (7, 2) interchanges coordinates and does not correspond to a standard single axis reflection. Option (2, 7) keeps the point unchanged, which would only be correct if the point were already on the y axis, which it is not.

Common Pitfalls: A common mistake is to change the wrong coordinate or both coordinates. Some learners mistakenly think reflection in the y axis changes y, but it is actually the x coordinate that changes sign. To avoid confusion, remember that the axis of reflection stays fixed, and the coordinate along that axis remains the same.

Final Answer: The reflection of (2, 7) across the y axis is (-2, 7).