The original coordinates of triangle ABC are:

The rule for reflection across the x-axis is $(x, y) \to (x, -y)$.

$$A_1 = (2, -3)$$ $$B_1 = (1, -1)$$ $$C_1 = (4, -1)$$

The rule for reflection across the y-axis is $(x, y) \to (-x, y)$.

$$A_2 = (-2, 3)$$ $$B_2 = (-1, 1)$$ $$C_2 = (-4, 1)$$

The rule for reflection across the line $y = x$ is $(x, y) \to (y, x)$.

$$A_3 = (3, 2)$$ $$B_3 = (1, 1)$$ $$C_3 = (1, 4)$$

The coordinates for the reflections are:

d) The coordinates of A₁, B₁, and C₁ are:

$$A_1 = \boxed{(2, -3)}$$ $$B_1 = \boxed{(1, -1)}$$ $$C_1 = \boxed{(4, -1)}$$

e) The coordinates of A₂, B₂, and C₂ are:

$$A_2 = \boxed{(-2, 3)}$$ $$B_2 = \boxed{(-1, 1)}$$ $$C_2 = \boxed{(-4, 1)}$$

f) The coordinates of A₃, B₃, and C₃ are:

$$A_3 = \boxed{(3, 2)}$$ $$B_3 = \boxed{(1, 1)}$$ $$C_3 = \boxed{(1, 4)}$$