Which rule describes the transformation that is a reflection in the x- axis?

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

I think the answer is b. Is this right?

To determine the rule that describes the transformation of a reflection in the x-axis, you need to understand what a reflection in the x-axis does.

A reflection in the x-axis is a transformation that flips a figure or point across the x-axis, while leaving the y-coordinate unchanged. This means that the x-coordinate remains the same, and only the y-coordinate changes its sign.

Looking at the given options:
a(x,y)=(y,x) - This rule represents a reflection across the line y=x, not the x-axis.
b(x,y)=(-x,y) - This rule reflects the point across the y-axis, not the x-axis.
c(x,y)=(-x,-y) - This rule represents a reflection across the origin.
d(x,y)=(x,-y) - This rule reflects the point across the x-axis by flipping the sign of the y-coordinate.

Therefore, the correct answer is d.

So, based on your explanation, the correct answer is d(x,y)=(x,-y).