Understanding Reflections over the Line y=x in Geometry: A Guide and Example

Reflection over y=x

To reflect a point or an object over the line y=x, we need to swap the x-coordinates with the y-coordinates

To reflect a point or an object over the line y=x, we need to swap the x-coordinates with the y-coordinates. This means that for every point (x, y), its reflected point (x’, y’) will have coordinates (y, x).

Let’s take an example to understand this better.

Suppose we have a point A with coordinates (3, 2). To reflect this point over the line y=x, we will swap the x and y coordinates:

New x-coordinate (x’) = 2
New y-coordinate (y’) = 3

Therefore, the reflected point A’ will have coordinates (2, 3).

We can also represent this reflection geometrically. The line y=x is a diagonal line with a slope of 1 passing through the origin. When a point is reflected over this line, it moves the same distance away from the line on the opposite side. The reflection is symmetric about the line y=x.

If we have a shape or an object, we will reflect each point individually using the same process and connect the new points to form the reflected shape.

It is important to note that reflection over the line y=x is a type of transformation in geometry. Transformations involve changing the position, size, or direction of an object without altering its shape. Reflection is just one type of transformation, and it can be used to flip or mirror objects over different lines or axes.

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