Question

identify a sequence of rigid transformations that would map (abcd
ightarrow abcd). give your answer in the form of a composition transformation mapping. (1 point) ((x,y)
ightarrow(x, -y - 4)) ((x,y)
ightarrow(-x,y - 4))

Explanation:

Step1: Analyze x - coordinates

The x - coordinates of the points in ABCD change sign to get the x - coordinates of the points in A''B''C''D''. For example, if a point in ABCD has x - coordinate \(x\), the corresponding point in A''B''C''D'' has x - coordinate \(-x\). This indicates a reflection across the y - axis, which is represented by the transformation \((x,y)\to(-x,y)\).

Step2: Analyze y - coordinates

The y - coordinates of the points in ABCD are decreased by 4 to get the y - coordinates of the points in A''B''C''D''. If a point in ABCD has y - coordinate \(y\), the corresponding point in A''B''C''D'' has y - coordinate \(y - 4\). This is a translation 4 units down, represented by the transformation \((x,y)\to(x,y - 4)\). Combining these two transformations, we first reflect across the y - axis and then translate 4 units down, resulting in the composition \((x,y)\to(-x,y - 4)\).

Answer:

\((x,y)\to(-x,y - 4)\)