How to write algebraic equations from word problems?

  see below

Step-by-step explanation:

Starting with B(-3, 0), it is relatively easy to try the points in the transformations and see what works.

First transformation: (-3, 0) ⇒ (-3+1, 0+1) = (-2, 1) ⇒ (1, -2) . . . . this one works

2nd transformation: (-3, 0) ⇒ (-2, 1) ⇒ (2, 1) . . . . nope

3rd transformation: (-3, 0) ⇒ (-3, 0) ⇒ (-1, 2) . . . . nope

4th transformation: (-3, 0) ⇒ (3, 0) ⇒ (5, 2) . . . . nope

Only the first transformation is a viable choice. We can check it with the other points:

  C(2, -1) ⇒ (3, 0) ⇒ (0, 3) . . . . matches C''(0, 3)

  D(-1, 2) ⇒ (0, 3) ⇒ (3, 0) . . . . matches D''(3, 0)

The appropriate transformation is the first one.