In this case, we'll have to carry out several steps to find the solution.
Data
RS :
R (-2 , 4)
S(-4 , -1)
R"S":
R"(3, -3)
S" (5 , 2)
Step 02:
We must check the options to find the solution.
A. reflection y = x (x ,y) ===> (y , x) , translation (x, y) ==> (x + 1 , y + 1)
R (-2 , 4) ==> R'(4 , -2) ===> R'' ( 5, -1)
S(-4 , -1) ===> S' (-1 , -4) ===> S" (0 , -3)
The transformation is not fulfilled.
B. rotation 180 (x,y) becomes (-x,-y) , translation (x, y) ==> (x + 1 , y + 1)
R (-2 , 4) ==> R'( 2 , -4) ===> R" ( 3 , -3)
S(-4 , -1) ===> S' (4 , 1) ===> S" (5 , 2)
The transformation is fulfilled.
The answer is:
B. rotation 180 (x,y) about the origin , translation (x, y) ==> (x + 1 , y + 1)