Question

What is the rule for the reflection?

a) Reflect over the y-axis: (x, y) → (-x, y)
b) Reflect over the y-axis: (x, y) → (x - 9, y)
c) Reflect over the x-axis: (x, y) → (-x, y)
d) Reflect over the x-axis: (x, y) → (x, -y)

Answer 1

The rule for reflection over the y-axis is (x, y) → (-x, y), and over the x-axis is (x, y) → (x, -y).

Step-by-step explanation:

The rule for reflection over the y-axis is: (x, y) → (-x, y). This means that the x-coordinate of a point is negated (multiplied by -1), while the y-coordinate remains unchanged. Conversely, the rule for reflection over the x-axis is: (x, y) → (x, -y), which implies that the y-coordinate of a point is negated, while the x-coordinate stays the same. These rules are essential in understanding the transformation of figures on a Cartesian coordinate system when they are reflected across one of the axes.