Identify the following composition transformation mapping: (x,y)→(−x,−y+5)

Question

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Option #1: rotate 180 degrees, then down 5

Option #2: reflect across the x-axis, then up 5

Option #3: reflect across the y-axis, then up 5

Option #4: rotate 180 degrees, then up 5

(1 point)

Answer 1

To identify the composition transformation mapping \((x,y) \rightarrow (-x, -y + 5)\), we can break it down into two steps.

1. The transformation \((x,y) \rightarrow (-x, -y)\) reflects the point across the origin, which is equivalent to a rotation of 180 degrees.

2. The next part, going from \((-x, -y)\) to \((-x, -y + 5)\), involves translating the point upwards by 5 units.

Putting these transformations together, the mapping involves rotating the point 180 degrees around the origin and then moving it up by 5 units.

Therefore, the correct option is:

Option #4: rotate 180 degrees, then up 5.