Question

1. select all possible series of rigid transformations that would take figure 2 onto figure 1.

a. reflect figure 2 over line ab and translate up 1.
b. translate figure 2 up 3, right 1, and reflect over line de.
c. reflect figure 2 over line ji, translate up 5, and reflect over line cd.
d. translate figure 2 up 2, reflect over line ab, and translate by directed line segment from d to g.

Explanation:

Step1: Analyze option a

If we reflect figure 2 over line \(AB\), the orientation will be wrong for aligning with figure 1. So option a is incorrect.

Step2: Analyze option b

Translate figure 2 up 3 and right 1. Looking at the coordinates of corresponding points (e.g., if we assume a coordinate - like system based on the grid), this translation will map figure 2 to figure 1.

Step3: Analyze option c

Reflecting figure 2 over line \(JI\) and then translating up 5. The reflection over \(JI\) changes the orientation, and then translating up 5 does not map figure 2 to figure 1.

Step4: Analyze option d

Translate figure 2 up 2, reflect over line \(AB\), and translate by the directed line segment \(DG\). The reflection over \(AB\) changes the orientation in a non - aligning way for mapping to figure 1.

Answer:

B. Translate figure 2 up 3, right 1, and reflect over line DE.