A Guide to Performing Reflections over the X-Axis in Mathematics

Reflection over x-axis

To perform a reflection over the x-axis, you need to change the sign of the y-coordinate of each point while keeping the x-coordinate the same

To perform a reflection over the x-axis, you need to change the sign of the y-coordinate of each point while keeping the x-coordinate the same.

Let’s consider an example. Suppose we have a point A with coordinates (3, 4). To reflect this point over the x-axis, we change the sign of the y-coordinate, making it -4, while leaving the x-coordinate unchanged. The new coordinates of the reflected point A’ are (3, -4).

If we have a shape, such as a line, polygon, or graph, we need to reflect each point individually. Let’s say we have a line segment with endpoints A(1, 2) and B(4, 5). To reflect this line segment over the x-axis, we would change the sign of the y-coordinate for each endpoint, resulting in A’ (1, -2) and B’ (4, -5).

For a graph, you may have multiple points, and all of them should be reflected. Let’s consider a simple graph of the equation y = x^2. To reflect this graph over the x-axis, we need to reflect each point on the graph. For example, the point (1, 1) will be reflected to (1, -1), the point (2, 4) will be reflected to (2, -4), and so on. Reflecting all the points will give you the reflected graph of this equation over the x-axis.

Remember, when reflecting over the x-axis, only the y-coordinates change while the x-coordinates remain the same.

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