Question
Identify the following composition transformation mapping: (x,y)→(−x,−y+5)
.
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)
.
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)
Answers
GPT-4o mini
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.**
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.**