What is the equation of the line of reflection for the transformation where (x, y) becomes (y, x)?

What is the equation of the line of reflection for the transformation where (x, y) becomes (y, x)?

• A. y = -x
• B. y = x
• C. y = 0
• D. x = y

Answer: (B)

The transformation where (x, y) becomes (y, x) describes a reflection across the line where the values of x and y are equal. This line is represented by the equation y = x. When reflecting a point across this line, the coordinates switch places, demonstrating that the original point at (x, y) will map to its reflection at (y, x), which aligns with the transformation defined in the question. In contrast, the other equations either do not represent lines of reflection related to this transformation or represent different types of reflections. For instance, y = -x would indicate a reflection that results in transformations of (x, y) to (-y, -x), which is not the case here. Thus, the equation y = x accurately depicts the line of reflection for the transformation specified in the question.

The transformation where (x, y) becomes (y, x) describes a reflection across the line where the values of x and y are equal. This line is represented by the equation y = x. When reflecting a point across this line, the coordinates switch places, demonstrating that the original point at (x, y) will map to its reflection at (y, x), which aligns with the transformation defined in the question.

In contrast, the other equations either do not represent lines of reflection related to this transformation or represent different types of reflections. For instance, y = -x would indicate a reflection that results in transformations of (x, y) to (-y, -x), which is not the case here. Thus, the equation y = x accurately depicts the line of reflection for the transformation specified in the question.