Understanding How to Reflect a Point or Shape over the Line y=x in Mathematics

Reflection over y=x

To understand how to reflect a point or a shape over the line y=x, it is helpful to first understand what the line represents

To understand how to reflect a point or a shape over the line y=x, it is helpful to first understand what the line represents. The line y=x is a diagonal line that passes through the origin (0,0) and has a slope of 1. This means that for any point (x, y) on the line, the x-coordinate and y-coordinate are equal (x = y).

To reflect a point (x, y) over the line y=x, you can simply switch the x-coordinate with the y-coordinate to get the reflected point (y, x). This is because the reflected point will have the same distance from the line y=x as the original point, but in the opposite direction.

For example, let’s say we have a point (2, 3). To reflect this point over the line y=x, we switch the x-coordinate with the y-coordinate, resulting in the reflected point (3, 2).

To reflect a shape (such as a triangle or a polygon) over the line y=x, you reflect each of its individual points using the above method. This will give you the corresponding reflected shape.

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