What is the result of reflecting a point across the line y = -x?

What is the result of reflecting a point across the line y = -x?

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

Answer: (B)

When reflecting a point across the line \( y = -x \), the coordinates of the original point \((x, y)\) are transformed in a specific manner. This reflection requires swapping the x-coordinate and y-coordinate while changing their signs. The transformation for a point \((x, y)\) reflected over the line \( y = -x \) results in the point \((-y, -x)\). This happens because: 1. The line \( y = -x \) has a slope of -1, meaning that it runs diagonally through the origin, creating equal angles with both axes. 2. Reflecting across this line effectively involves both switching the coordinates and inverting their signs, since the line suggests a mirror-like behavior in relation to the origin. Thus, the correct outcome of reflecting \((x, y)\) across the line \( y = -x \) is represented by the transformation \((-y, -x)\), confirming that the answer is indeed option B.

When reflecting a point across the line ( y = -x ), the coordinates of the original point ((x, y)) are transformed in a specific manner. This reflection requires swapping the x-coordinate and y-coordinate while changing their signs.

The transformation for a point ((x, y)) reflected over the line ( y = -x ) results in the point ((-y, -x)). This happens because:

1. The line ( y = -x ) has a slope of -1, meaning that it runs diagonally through the origin, creating equal angles with both axes.

2. Reflecting across this line effectively involves both switching the coordinates and inverting their signs, since the line suggests a mirror-like behavior in relation to the origin.

Thus, the correct outcome of reflecting ((x, y)) across the line ( y = -x ) is represented by the transformation ((-y, -x)), confirming that the answer is indeed option B.