,

## Translating Five Units Down: Understanding the Vertical Translation Equation

In the world of mathematics, transformations play a vital role in manipulating geometrical figures. One such transformation is translation, which involves moving a figure from its original position to a new one without changing its size or shape. Vertical translation, specifically, involves moving a figure up or down along the y-axis.

### Identifying the Vertical Translation Equation

To identify the equation that translates a figure five units down, we need to understand the concept of transformation equations. A transformation equation is a mathematical expression that describes the movement of a figure from one position to another. For vertical translation, the equation takes the following form:

```
(x, y) -> (x, y - 5)
```

### What the Equation Means

This equation means that every point (x, y) in the original figure will be moved down by five units in the translated figure. The x-coordinate remains unchanged, as the movement is only vertical. The y-coordinate, however, is reduced by 5, effectively shifting the figure down along the y-axis.

### Example

Consider a square with vertices at (1, 2), (1, 5), (4, 5), and (4, 2). To translate this square five units down, we simply apply the translation equation to each vertex:

```
(1, 2) -> (1, 2 - 5) = (1, -3)
(1, 5) -> (1, 5 - 5) = (1, 0)
(4, 5) -> (4, 5 - 5) = (4, 0)
(4, 2) -> (4, 2 - 5) = (4, -3)
```

The translated square will now have vertices at (1, -3), (1, 0), (4, 0), and (4, -3).

### Applications of Vertical Translation

Vertical translation is widely used in various fields, including:

**Computer graphics:**Translating objects up or down in 3D animations.**Robotics:**Moving robotic arms or other components vertically.**Physics:**Simulating the vertical motion of objects in projectile motion.

### Conclusion

Understanding the equation that translates five units down is crucial for performing vertical translation transformations in geometry and its applications. The equation, (x, y) -> (x, y – 5), represents a downward movement of every point in a figure by five units along the y-axis. By applying this equation, we can effectively shift figures vertically while maintaining their original size and shape.

### FAQs

**What is the general equation for a vertical translation of k units?**

- (x, y) -> (x, y – k)

**How does vertical translation affect the x-coordinate?**

- It remains unchanged.

**What is the purpose of vertical translation equations?**

- To describe the movement of a figure up or down along the y-axis.

**Can vertical translation equations be used to move a figure upward?**

- Yes, by using a positive value for k in the equation.

**How is vertical translation applied in real-world scenarios?**

- In computer graphics, robotics, and physics simulations.

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Identify,Equation,That,Translates,Five,Units,Down