Question

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

Explanation:

Step1: Analyze x - coordinate change

Let's assume a general point \((x,y)\) on \(ABCD\). For the x - coordinate, we need to consider reflection and translation. If we first reflect a point \((x,y)\) over the y - axis, the transformation is \((x,y)\to(-x,y)\). Then, if we translate the reflected point 4 units to the left, the x - coordinate of the new point becomes \(-x - 4\). The y - coordinate remains the same throughout these two rigid transformations.

Step2: Check the mapping

The transformation \((x,y)\to(-x - 4,y)\) is a composition of a reflection over the y - axis (\((x,y)\to(-x,y)\)) followed by a translation 4 units to the left. This mapping will map the figure \(ABCD\) to \(A''B''C''D''\) as required by rigid transformations.

Answer:

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