Difficulty: Easy
Correct Answer: (-2, -3.5)
Explanation:
Introduction / Context:
This question involves reflections in the coordinate plane, a fundamental concept in analytic geometry. Reflecting a point in the y-axis means producing a mirror image of that point across the vertical axis. Understanding the rule for how coordinates change under such reflections is essential for many geometry and transformation problems.
Given Data / Assumptions:
Concept / Approach:
Reflection in the y-axis changes the sign of the x-coordinate but leaves the y-coordinate unchanged. In general:
If P(x, y) is reflected in the y-axis, then P' = (−x, y).
This is because the y-axis is the line x = 0, and reflecting across it flips left and right while keeping vertical position constant.
Step-by-Step Solution:
We have P(2, -3.5).
Under reflection in the y-axis, x → −x and y stays the same.
So new x-coordinate = −2.
New y-coordinate remains −3.5.
Therefore, the reflected point is (−2, −3.5).
Verification / Alternative check:
Plotting roughly in your mind, point (2, -3.5) lies to the right of the y-axis and below the x-axis. Its reflection should lie at the same vertical level, but the same distance to the left of the y-axis, that is at x = -2. This matches the coordinate (−2, −3.5).
Why Other Options Are Wrong:
(-2, 3.5) corresponds to reflection in both axes combined (a half-turn), not just the y-axis. (-3.5, -2) and (3.5, -2) swap x and y, which is typical of reflection across the line y = x or similar transformations, not reflection across the y-axis.
Common Pitfalls:
A common mistake is to flip the wrong coordinate or both coordinates. Another error is to confuse reflection in the x-axis with reflection in the y-axis. Remember: reflection in the y-axis changes the sign of x, reflection in the x-axis changes the sign of y.
Final Answer:
The reflection of (2, -3.5) in the y-axis is (-2, -3.5).
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