Question

Ejemplos of translation in polygons

Answer 1

Translation in the context of polygons refers to moving a polygon from one position to another without changing its shape, size, or orientation. Here are a few examples of translations involving different types of polygons:

### Example 1: Triangle Translation
**Original Triangle Vertices:**
- A(1, 2)
- B(3, 4)
- C(5, 1)

**Translation Vector:**
- T(2, 3)

**Translated Triangle Vertices:**
- A'(1 + 2, 2 + 3) = A'(3, 5)
- B'(3 + 2, 4 + 3) = B'(5, 7)
- C'(5 + 2, 1 + 3) = C'(7, 4)

### Example 2: Square Translation
**Original Square Vertices:**
- D(0, 0)
- E(0, 2)
- F(2, 2)
- G(2, 0)

**Translation Vector:**
- T(-1, 1)

**Translated Square Vertices:**
- D'(-1, 0 + 1) = D'(-1, 1)
- E'(-1, 2 + 1) = E'(-1, 3)
- F'(-1 + 2, 2 + 1) = F'(1, 3)
- G'(-1 + 2, 0 + 1) = G'(1, 1)

### Example 3: Rectangle Translation
**Original Rectangle Vertices:**
- H(2, 3)
- I(2, 6)
- J(5, 6)
- K(5, 3)

**Translation Vector:**
- T(4, -2)

**Translated Rectangle Vertices:**
- H'(2 + 4, 3 - 2) = H'(6, 1)
- I'(2 + 4, 6 - 2) = I'(6, 4)
- J'(5 + 4, 6 - 2) = J'(9, 4)
- K'(5 + 4, 3 - 2) = K'(9, 1)

### General Formula for Translation
For any point (x, y) and a translation vector (a, b), the new coordinates after translation are given by:
- (x', y') = (x + a, y + b)

Translation is a simple geometrical transformation that keeps the properties of the shape intact while moving it to a new location on the coordinate plane.