Question

rotations: rotations counter - clockwise about the origin rotations of 90°: (x,y)→(−y,x) rotations of 180°: (x,y)→(−x,−y) rotations of 270°: (x,y)→(y,−x) reflections: across the x - axis across the y - axis the _ - coordinate changes to its _ the _ - coordinate changes to its _ (x,y)→(_) (x,y)→(_) across y = x across y = - x the coordinates _ the coordinates _ and become _ (x,y)→(_) (x,y)→(___)

Explanation:

Step1: Reflection across x - axis

The y - coordinate changes to its opposite. If we have a point \((x,y)\), after reflection across the x - axis, the transformation is \((x,y)\to(x, - y)\).

Step2: Reflection across y - axis

The x - coordinate changes to its opposite. For a point \((x,y)\), after reflection across the y - axis, the transformation is \((x,y)\to(-x,y)\).

Step3: Reflection across \(y = x\)

The coordinates swap. So for a point \((x,y)\), after reflection across \(y=x\), the transformation is \((x,y)\to(y,x)\).

Step4: Reflection across \(y=-x\)

The coordinates swap and become opposite. For a point \((x,y)\), after reflection across \(y =-x\), the transformation is \((x,y)\to(-y,-x)\).

Answer:

Across the x - axis: y, opposite, \((x,-y)\)
Across the y - axis: x, opposite, \((-x,y)\)
Across \(y = x\): swap, \((y,x)\)
Across \(y=-x\): swap, opposite, \((-y,-x)\)