Understanding Reflections over the x-axis: Flipped Figures with Same Shape and Size

Reflection over x-axis

When a figure or point is reflected over the x-axis, it essentially results in a flipped image where the new figure has the same size and shape but is positioned on the opposite side of the x-axis

When a figure or point is reflected over the x-axis, it essentially results in a flipped image where the new figure has the same size and shape but is positioned on the opposite side of the x-axis. This reflection occurs by maintaining the same distance between the original figure and the x-axis but changing the sign of the y-coordinate.

To reflect a point (x, y) over the x-axis, you can simply change the sign of the y-coordinate. The new point will have the same x-coordinate but a negative y-coordinate, resulting in (x, -y). For example, if you have a point (3, 4), the reflection over the x-axis would be (3, -4).

If you have a figure composed of multiple points, you would need to reflect each point individually. Consider the figure shown below:

“`
(2, 3) (4, 5)
x ————- x
|
| (3, 4)
|
x ————– x
(-2, -5) (-4, -2)
“`

To reflect this figure over the x-axis, you would change the sign of the y-coordinate for each point:

“`
(2, 3) (4, 5)
x ————– x
|
| (3, -4)
|
x ————– x
(-2, -5) (-4, -2)
“`

As you can see, the figure has been flipped with respect to the x-axis, maintaining the same size and shape.

It’s important to note that when reflecting a figure over the x-axis, the x-coordinate remains unchanged. Only the sign of the y-coordinate is flipped. This transformation is known as a reflection because the image created is mirrored or reflected across the x-axis.

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