Learn How To Perform X-Axis Reflections On A Coordinate Plane – A Step-By-Step Guide

Reflection over x – axis

y = f(x) -> y = -f(x); (x,y) -> (x,-y)

When a reflection is performed over the x-axis, it means that each point in the original figure is mirrored across the x-axis to create a new image. The x-coordinates of each point in the original figure are kept the same, but the y-coordinates are negated (or multiplied by -1) in order to create the new image.

To perform a reflection over the x-axis, we can follow these steps:
1. Draw the original figure on a coordinate plane.
2. Draw the x-axis below the figure.
3. For each point in the figure, reflect it across the x-axis by negating the y-coordinate (e.g. (x, y) becomes (x, -y)).
4. Connect the reflected points to create the new image.

For example, consider the triangle with vertices at (2, 4), (4, 2), and (6, 4). To reflect this triangle over the x-axis, we would negate the y-coordinates to get the new vertices: (2, -4), (4, -2), and (6, -4). We can then connect these reflected points to create the new image of the triangle.

It is important to note that reflecting over the x-axis is a type of transformation that preserves the orientation of the original figure. This means that if the original figure was clockwise, then the reflected image will also be clockwise. Likewise, if the original figure was counterclockwise, then the reflected image will also be counterclockwise.

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