Question
the line of reflection is horizontal meaning
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GPT-4o mini
When the line of reflection is horizontal, it means that the line runs left to right across the plane without slanting up or down. In a two-dimensional Cartesian coordinate system, this would typically mean that the line is parallel to the x-axis.
For example, if the line of reflection is the line \( y = k \) (where \( k \) is a constant), it will be a horizontal line. Reflecting a point across this line will result in a point that is equidistant from the line on the opposite side.
If you have a point \( (x, y) \) and you want to reflect it over the horizontal line \( y = k \), the coordinates of the reflected point \( (x', y') \) would be:
- \( x' = x \) (the x-coordinate remains the same)
- \( y' = 2k - y \) (the y-coordinate is adjusted to be equidistant from the line)
Overall, the idea of a horizontal line of reflection is crucial in geometry, particularly in understanding symmetry and transformations.
For example, if the line of reflection is the line \( y = k \) (where \( k \) is a constant), it will be a horizontal line. Reflecting a point across this line will result in a point that is equidistant from the line on the opposite side.
If you have a point \( (x, y) \) and you want to reflect it over the horizontal line \( y = k \), the coordinates of the reflected point \( (x', y') \) would be:
- \( x' = x \) (the x-coordinate remains the same)
- \( y' = 2k - y \) (the y-coordinate is adjusted to be equidistant from the line)
Overall, the idea of a horizontal line of reflection is crucial in geometry, particularly in understanding symmetry and transformations.