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

Answer 1

To identify the composition transformation mapping given by \((x,y) \to (-x, -y + 5)\), we need to analyze the effects of each component of the transformation.

1. The first part, \((x,y) \to (-x, -y)\), corresponds to reflecting across the origin (or equivalently, rotating 180 degrees around the origin). This changes both the x-coordinate and the y-coordinate - effectively reversing their signs.

2. The second part, \((-x, -y) \to (-x, -y + 5)\), translates the resulting point up by 5 units along the y-axis.

Putting it all together, the transformation first rotates the point 180 degrees (reflecting across the origin) and then moves it up 5 units.

Based on this analysis, the correct description of the transformation is:

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