Identify the following composition trans

Question

formation mapping: (x,y)→(−x,−y+5)

Answer 1

The transformation mapping given by \((x, y) \rightarrow (-x, -y + 5)\) can be analyzed as follows:

1. Reflection: The first part of the transformation, \((x, y) \rightarrow (-x, y)\), represents a reflection across the \(y\)-axis. This transforms the point \((x, y)\) into \((-x, y)\).

2. Vertical Reflection and Translation: The second part of the transformation, from \((-x, y)\) to \((-x, -y + 5)\), can be broken down into two actions:

   • The transformation \(( -x, y) \rightarrow (-x, -y)\) reflects the point across the \(x\)-axis.
   • Then, the transformation \((-x, -y) \rightarrow (-x, -y + 5)\) translates the point vertically upwards by 5 units.

Putting it all together, the complete transformation can be described as:

1. Reflect across the \(y\)-axis.
2. Reflect across the \(x\)-axis.
3. Translate vertically upward by 5 units.

In simpler terms, the overall transformation first flips the point across the \(y\)-axis, flips it again across the \(x\)-axis, and then shifts it up by 5 units.