Question

If a reflection in the line y=−x occurs, then the rule for this reflection is _____.

a) (x,y)→(x,-y)
b) (x,y)-→-x,y)
c) (x,y)→(x,y)
d) (x,y)→(-x,-y)

Answer 1

The correct rule for a reflection in the line y = -x is (x,y) → (-y,-x), which involves swapping and negating both coordinates.

Step-by-step explanation:

When a reflection occurs in the line y = -x, each point (x, y) on a figure is transformed to a new point where the x-coordinate and y-coordinate values are swapped and their signs are changed. Thus, the correct rule for this reflection is (x,y) → (-y,-x). This can be further understood by visualizing that a point on the coordinate plane that is reflected over the line y = -x would have its x-value become the negative y-value and its y-value become the negative x-value after the transformation, performing a rotation in the counterclockwise direction from the positive x direction of the coordinate system. Remember that for a reflection across a line like y = -x, the coordinates flip and the signs of the flipped coordinates are negated.