Identify The Equation That Translates Five Units Down

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Identify The Equation That Translates Five Units Down

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.

Vertical Translation Equation

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

  1. What is the general equation for a vertical translation of k units?
  • (x, y) -> (x, y – k)
  1. How does vertical translation affect the x-coordinate?
  • It remains unchanged.
  1. What is the purpose of vertical translation equations?
  • To describe the movement of a figure up or down along the y-axis.
  1. Can vertical translation equations be used to move a figure upward?
  • Yes, by using a positive value for k in the equation.
  1. 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

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