Question

reflections
over the x - axis: (x, y) → (x, -y)
over the y - axis: (x, y) → (-x, y)
over the line y = x: (x, y) → (y, x)

Explanation:

Step1: Identify the Discipline and Subfield

The problem involves reflections of points in a coordinate plane, which falls under Geometry (a subfield of Mathematics).

Step2: Recall Reflection Rules

• Reflection over x - axis: For a point \((x,y)\), the reflection is \((x, -y)\). This is because when we reflect over the x - axis, the x - coordinate remains the same and the y - coordinate changes its sign.
• Reflection over y - axis: For a point \((x,y)\), the reflection is \((-x,y)\). Here, the y - coordinate remains the same and the x - coordinate changes its sign.
• Reflection over the line \(y = x\): For a point \((x,y)\), the reflection is \((y,x)\). This is because the line \(y=x\) swaps the x and y coordinates of a point.

Answer:

The image provides the rules for reflecting a point \((x,y)\) over the x - axis \((x,y)\to(x, -y)\), over the y - axis \((x,y)\to(-x,y)\), and over the line \(y = x\) \((x,y)\to(y,x)\) in the context of coordinate geometry (subfield: Geometry, discipline: Mathematics).