A reflection over the line y = x maps a point (x, y) to which ordered pair?

A reflection over the line y = x maps a point (x, y) to which ordered pair?

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

Answer: (C)

Reflecting across the line y = x swaps the x- and y-coordinates of a point. So a point (x, y) becomes (y, x). This makes sense because the line y = x is the set of points where the two coordinates are equal, and the mirror image across that line flips the horizontal and vertical positions of the point. For example, (3, -4) would map to (-4, 3). The other transformations represent different moves: flipping to (-x, -y) is a 180-degree turn around the origin; (y, -x) is a 90-degree rotation; and (-y, -x) is a reflection across the line y = -x. Therefore, the mapping that matches reflection over y = x is (y, x).

Reflecting across the line y = x swaps the x- and y-coordinates of a point. So a point (x, y) becomes (y, x). This makes sense because the line y = x is the set of points where the two coordinates are equal, and the mirror image across that line flips the horizontal and vertical positions of the point. For example, (3, -4) would map to (-4, 3). The other transformations represent different moves: flipping to (-x, -y) is a 180-degree turn around the origin; (y, -x) is a 90-degree rotation; and (-y, -x) is a reflection across the line y = -x. Therefore, the mapping that matches reflection over y = x is (y, x).