Determining the reflection of a point across the line y = x results in which transformation?

Determining the reflection of a point across the line y = x results in which transformation?

• A. (x,y) = (y,-x)
• B. (x,y) = (y,x)
• C. (x,y) = (-y,x)
• D. (x,y) = (x,-y)

Answer: (B)

When reflecting a point across the line \( y = x \), the coordinates of the point undergo a specific transformation. The line \( y = x \) acts as a mirror, meaning that for any point represented as \( (x, y) \), swapping its coordinates will produce the reflection. In this case, if the original point is \( (x, y) \), the reflection across the line \( y = x \) will result in the point \( (y, x) \). This shift effectively means that the x-coordinate of the original point becomes the y-coordinate of the new point and vice versa. Thus, the correct transformation that describes this reflection is represented as \( (x, y) = (y, x) \). This demonstrates how the coordinates are interchanged during the reflection process.

When reflecting a point across the line ( y = x ), the coordinates of the point undergo a specific transformation. The line ( y = x ) acts as a mirror, meaning that for any point represented as ( (x, y) ), swapping its coordinates will produce the reflection.

In this case, if the original point is ( (x, y) ), the reflection across the line ( y = x ) will result in the point ( (y, x) ). This shift effectively means that the x-coordinate of the original point becomes the y-coordinate of the new point and vice versa.

Thus, the correct transformation that describes this reflection is represented as ( (x, y) = (y, x) ). This demonstrates how the coordinates are interchanged during the reflection process.