Translations of triangles on coordinate planes.

To solve the problem of translating geometric shapes on a coordinate plane, we need to apply the given translation vectors to each vertex of the shapes. Let's go through each part step by step.

General Approach:

1. Identify the coordinates of each vertex of the shape.
2. Apply the translation vector to each vertex.
3. Plot the new coordinates to form the translated shape.

Translation Rules:

- If the translation vector is \((a, b)\), then for any point \((x, y)\):
\[
(x, y) \rightarrow (x + a, y + b)
\]

---

Part (i): Translation \((-2, -1)\)

#### Original Shape:
Assume the vertices of the original triangle are:
\[
A(1, 3), \quad B(4, 3), \quad C(2, 5)
\]

#### Apply Translation \((-2, -1)\):
- For \(A(1, 3)\):
\[
(1 + (-2), 3 + (-1)) = (-1, 2)
\]
- For \(B(4, 3)\):
\[
(4 + (-2), 3 + (-1)) = (2, 2)
\]
- For \(C(2, 5)\):
\[
(2 + (-2), 5 + (-1)) = (0, 4)
\]

#### New Coordinates:
\[
A'(-1, 2), \quad B'(2, 2), \quad C'(0, 4)
\]

#### Plot the new points and connect them to form the translated triangle.

---

Part (ii): Translation \((6, 0)\)

#### Original Shape:
Assume the vertices of the original triangle are:
\[
A(1, 2), \quad B(3, 4), \quad C(5, 2)
\]

#### Apply Translation \((6, 0)\):
- For \(A(1, 2)\):
\[
(1 + 6, 2 + 0) = (7, 2)
\]
- For \(B(3, 4)\):
\[
(3 + 6, 4 + 0) = (9, 4)
\]
- For \(C(5, 2)\):
\[
(5 + 6, 2 + 0) = (11, 2)
\]

#### New Coordinates:
\[
A'(7, 2), \quad B'(9, 4), \quad C'(11, 2)
\]

#### Plot the new points and connect them to form the translated triangle.

---

Part (iii): Translation \((0, -4)\)

#### Original Shape:
Assume the vertices of the original triangle are:
\[
A(2, 5), \quad B(4, 3), \quad C(2, 1)
\]

#### Apply Translation \((0, -4)\):
- For \(A(2, 5)\):
\[
(2 + 0, 5 + (-4)) = (2, 1)
\]
- For \(B(4, 3)\):
\[
(4 + 0, 3 + (-4)) = (4, -1)
\]
- For \(C(2, 1)\):
\[
(2 + 0, 1 + (-4)) = (2, -3)
\]

#### New Coordinates:
\[
A'(2, 1), \quad B'(4, -1), \quad C'(2, -3)
\]

#### Plot the new points and connect them to form the translated triangle.

---

Part (iv): Translation \((-7, -3)\)

#### Original Shape:
Assume the vertices of the original triangle are:
\[
A(3, 4), \quad B(5, 2), \quad C(7, 4)
\]

#### Apply Translation \((-7, -3)\):
- For \(A(3, 4)\):
\[
(3 + (-7), 4 + (-3)) = (-4, 1)
\]
- For \(B(5, 2)\):
\[
(5 + (-7), 2 + (-3)) = (-2, -1)
\]
- For \(C(7, 4)\):
\[
(7 + (-7), 4 + (-3)) = (0, 1)
\]

#### New Coordinates:
\[
A'(-4, 1), \quad B'(-2, -1), \quad C'(0, 1)
\]

#### Plot the new points and connect them to form the translated triangle.

---

Final Answer:

\[
\boxed{
\text{(i) } A'(-1, 2), B'(2, 2), C'(0, 4) \\
\text{(ii) } A'(7, 2), B'(9, 4), C'(11, 2) \\
\text{(iii) } A'(2, 1), B'(4, -1), C'(2, -3) \\
\text{(iv) } A'(-4, 1), B'(-2, -1), C'(0, 1)
}
\]