The point (-5, -9) was reflected over an axis to become the point (5, -9). Which axis was it reflected over?
A. x-axis, because the x-coordinate is the opposite
B. x-axis, because the y-coordinate is the opposite
C. y-axis, because the x-coordinate is the opposite
D. y-axis, because the y-coordinate is the opposite
Answer (2)
The x-coordinate changes sign: − 5 → 5 .
The y-coordinate remains the same: − 9 → − 9 .
Reflection over the y-axis changes the sign of the x-coordinate and keeps the y-coordinate the same.
The point was reflected over the y-axis .
Explanation
Problem Analysis Let's analyze the given points and the reflection rules to determine the axis of reflection.
Reflection Rules The original point is (-5, -9) and the reflected point is (5, -9).
When a point is reflected over the x-axis, the x-coordinate remains the same, and the y-coordinate changes its sign. For example, the reflection of (x, y) over the x-axis is (x, -y).
When a point is reflected over the y-axis, the y-coordinate remains the same, and the x-coordinate changes its sign. For example, the reflection of (x, y) over the y-axis is (-x, y).
Applying Reflection Rules to the Given Points In this case, the x-coordinate of the point changed from -5 to 5, while the y-coordinate remained the same at -9. This indicates that the point was reflected over the y-axis.
Conclusion Therefore, the point (-5, -9) was reflected over the y-axis to become the point (5, -9).
Examples
Reflections are used in creating symmetrical designs in art and architecture. For example, if you are designing a building and want it to be symmetrical, you can reflect one half of the design over a central axis to create the other half. This ensures that both sides of the building are mirror images of each other, providing a balanced and aesthetically pleasing appearance. Understanding reflections helps in various fields like computer graphics, physics, and even everyday tasks like using a mirror.
The point (-5, -9) was reflected over the y-axis to become (5, -9) because the x-coordinate changed sign while the y-coordinate remained the same. Hence, the correct answer is option D. This indicates that when reflecting over the y-axis, the x-coordinate is the only one affected.
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