What is the reflection of the point (2, -3.5) in the y-axis in the Cartesian coordinate plane?

Introduction / Context:
This problem is from coordinate geometry and deals with reflections of points across one of the coordinate axes. Reflections are basic transformations that flip points across a line, such as the x-axis, y-axis, or the origin. Knowing how the coordinates change under these reflections is very useful in both pure mathematics and applications such as graphics and physics simulations. Here, you are asked to reflect a point across the y-axis.

Given Data / Assumptions:

• The original point is P(2, -3.5).
• The reflection is taken in the y-axis.
• The y-axis is the vertical line defined by x = 0.
• We must find the coordinates of the reflected point P prime.
• We assume standard Cartesian coordinates with the usual reflection rules.

Concept / Approach:
Reflecting a point across the y-axis keeps the y coordinate the same but reverses the sign of the x coordinate. Geometrically, the point is flipped horizontally across the line x = 0, so it ends up the same distance from the y-axis but on the opposite side. In algebraic terms, reflecting (x, y) in the y-axis transforms it to (-x, y). We simply apply this rule to the given coordinates to find the new point.

Step-by-Step Solution:
Original point P has coordinates (x, y) = (2, -3.5).Reflection in the y-axis maps (x, y) to (-x, y).So the reflected point P prime is (-2, -3.5).The x coordinate has changed sign from 2 to -2, while the y coordinate remains -3.5.Therefore, the reflection of (2, -3.5) in the y-axis is (-2, -3.5).

Verification / Alternative check:
Visualise the point (2, -3.5) on a coordinate grid. It is 2 units to the right of the y-axis and 3.5 units below the x-axis. Reflecting across the y-axis should move the point 2 units to the left of the y-axis while keeping the vertical position unchanged. That is exactly the point (-2, -3.5). The distance from the y-axis remains 2 units, but on the opposite side, which confirms that the reflection rule has been applied correctly.

Why Other Options Are Wrong:
Option (-2, 3.5) reflects the point across both axes, not just the y-axis. Option (-3.5, -2) swaps the x and y coordinates and then changes signs, which corresponds to a rotation or reflection across a different line. Option (3.5, -2) similarly mixes up coordinates and reflections. Option (2, 3.5) reflects across the x-axis, not the y-axis. None of these match the pure y-axis reflection rule (x, y) to (-x, y) for the point (2, -3.5).

Common Pitfalls:
Students sometimes confuse reflections in the x-axis and y-axis, accidentally changing the wrong coordinate. Another typical error is to change the sign of both coordinates, which corresponds to rotation by 180 degrees about the origin rather than a single axis reflection. Remember that reflection in the y-axis affects only the x coordinate, and reflection in the x-axis affects only the y coordinate. Keeping this distinction clear makes such problems easy to handle.

Final Answer:
The reflection of the point (2, -3.5) in the y-axis is (-2, -3.5).