Question

in the diagram below, congruent figures 1, 2, and 3 are drawn. which sequence of transformations maps figure 1 onto figure 2 and then figure 2 onto figure 3? 1) a reflection followed by a translation 2) a rotation followed by a translation 3) a translation followed by a reflection 4) a translation followed by a rotation

Explanation:

Step1: Analyze the transformation from figure 1 to figure 2

A reflection over the \(y -\)axis maps figure 1 onto figure 2. The \(x -\)coordinates of the vertices of figure 1 change their signs to get the vertices of figure 2 (for example, if a point in figure 1 has coordinates \((x,y)\), the corresponding point in figure 2 has coordinates \((-x,y)\) after reflection over the \(y -\)axis).

Step2: Analyze the transformation from figure 2 to figure 3

A translation (a slide) maps figure 2 onto figure 3. The \(y -\)coordinates of the vertices of figure 2 are decreased by a certain amount (the figure is moved downwards) and the \(x -\)coordinates are changed (the figure is moved to the right or left).

Answer:

1. a reflection followed by a translation