Question

What is the rule for the reflection?

a.ry-axis(x, y) → (–x, y)
b.ry-axis(x, y) → (x, –y)
c.rx-axis(x, y) → (–x, y)
d.rx-axis(x, y) → (x, –y)

Answer 1

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed). ... the line y = x is the point (y, x). The reflection of the point (x,y) across. the line y = -x is the point (-y, -x)

Answer 2

D.
`\text{rx-axis}(x,y)\rightarrow (x,-y)`.

Explanation:

We have been been given an image of reflection on coordinate plane and we are asked to find the rule for the given reflection.

Upon looking at our given image, we can see that its vertices are A(-1,0), B(0,2), C(3,2) and D(4,0).

The vertices of pre-image are A'(-1,0), B(0,-2), C(3,-2) and D(4,0).

Since the x-coordinate are same and y-coordinates has changed to their opposite sign, therefore, the given image is reflected across x-axis to get the pre-image.

The rule of reflection an image across x-axis is
`\text{rx-axis}(x,y)\rightarrow (x,-y)`.

Therefore, option D is the correct choice.