How To Reflect A Point Over The Line Y=X: Step-By-Step Guide

Reflection over y=x

This is an example of this rigid motion transformation.

When we reflect a point over the line y=x, we are essentially swapping its x and y-coordinates while keeping its position relative to the line y=x unchanged. In other words, if a point (x, y) lies on the line y=x, its reflection over the line y=x will be the point (y, x).

To reflect a point over the line y=x, we can follow these steps:

1. Step 1: Plot the point and draw the line y=x on the coordinate plane

2. Step 2: Draw a perpendicular line from the point to the line y=x.

3. Step 3: The intersection of the perpendicular line with y=x represents the midpoint of the segment connecting the point and its reflection.

4. Step 4: Draw a line segment connecting the point and its reflection, ensuring that this segment is perpendicular to the line y=x.

5. Step 5: Label the coordinates of the reflected point, which should be the point (y, x).

For example, let’s say we want to reflect the point (3, 4) over the line y=x.

1. We would plot the point (3, 4) and draw the line y=x.

2. We would draw a perpendicular line from the point (3, 4) to the line y=x. This line would cross y=x at the point (4, 3), which is the midpoint of the segment connecting (3, 4) and its reflection.

3. We would draw a line segment connecting (3, 4) and (4, 3), ensuring that this segment is perpendicular to the line y=x.

4. Finally, we would label the coordinates of the reflected point, which is (4, 3).

Therefore, the reflection of the point (3, 4) over the line y=x is the point (4, 3).

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