Question

write a sequence of rigid motions that maps AB to XY

Answer 1

x=-a-1
y=b
so t(x,y)=(-x-1,y)

check it for example a
a(2,-2) t(a)=t(2,-2)=(-2-1,-2)=x

Answer 2

another method to answer is
suppose t(x,y)=ax+by
apply 2 point in t(x,y)
and solve the system of equation
then you have the map