Applying the Translation Rule to Point B

Oct 13, 2025 by miodeya.com 94 views

Understanding the Translation Rule

When a point is translated according to a given rule, its coordinates change based on the specific transformation applied. In this case, the translation rule is ${$ (x, y) \rightarrow (x+2, y-8)$}$, which means that every point (x, y) in the original coordinate system is moved to a new location (x+2, y-8) in the translated coordinate system.

Applying the Translation Rule to Point B

To find the coordinates of point B', we need to apply the translation rule to the pre-image coordinates of point B, which are given as ${$ (4, -5)$}$. Using the translation rule, we can calculate the new coordinates of point B' as follows:

The x-coordinate of point B' is obtained by adding 2 to the x-coordinate of point B: ${ $4 + 2 = 6\$}$ .
The y-coordinate of point B' is obtained by subtracting 8 from the y-coordinate of point B: ${$ -5 - 8 = -13$}$.

Determining the Coordinates of Point B'

Based on the calculations above, the coordinates of point B' are ${$ (6, -13)$}$. This means that point B has been translated 2 units to the right and 8 units down to reach its new location.

Conclusion

In conclusion, the translation rule ${$ (x, y) \rightarrow (x+2, y-8)$}$ has been applied to the pre-image coordinates of point B ${$ (4, -5)$}$ to find the coordinates of point B'. The resulting coordinates are ${$ (6, -13)$}$, indicating that point B has been translated 2 units to the right and 8 units down.

Example Use Case

This translation rule can be applied to various geometric transformations, such as translating triangles, quadrilaterals, or other polygons. By understanding how to apply translation rules, mathematicians and students can analyze and solve problems involving geometric transformations.

Key Takeaways

The translation rule ${$ (x, y) \rightarrow (x+2, y-8)$}$ is applied to the pre-image coordinates of point B ${$ (4, -5)$}$ to find the coordinates of point B'.
The resulting coordinates of point B' are ${$ (6, -13)$}$, indicating that point B has been translated 2 units to the right and 8 units down.
This translation rule can be applied to various geometric transformations, such as translating triangles, quadrilaterals, or other polygons.

Further Exploration

For further exploration, consider the following questions:

What happens when the translation rule is applied to a point that is already at the origin (0, 0)?
How does the translation rule change when the x and y components are swapped?
Can the translation rule be applied to a point that is not a single point, but rather a set of points or a polygon?

By exploring these questions and applying the translation rule to various geometric transformations, mathematicians and students can deepen their understanding of geometric transformations and develop problem-solving skills.

Understanding the Translation Rule

Q&A: Translation Rule

Q: What is the purpose of the translation rule?

A: The translation rule is used to describe how points in the original coordinate system are moved to new locations in the translated coordinate system.

Q: How does the translation rule change the coordinates of a point?

A: The translation rule changes the coordinates of a point by adding 2 to the x-coordinate and subtracting 8 from the y-coordinate.

Q: Can the translation rule be applied to any point in the coordinate system?

A: Yes, the translation rule can be applied to any point in the coordinate system.

Q: What happens when the translation rule is applied to a point that is already at the origin (0, 0)?

A: When the translation rule is applied to a point that is already at the origin (0, 0), the new coordinates of the point will be (2, -8).

Q: How does the translation rule change when the x and y components are swapped?

A: If the x and y components are swapped, the translation rule becomes ${$ (y, x) \rightarrow (y+2, x-8)$}$.

Q: Can the translation rule be applied to a point that is not a single point, but rather a set of points or a polygon?

A: Yes, the translation rule can be applied to a point that is not a single point, but rather a set of points or a polygon.

Q&A: Point B'

Q: What are the coordinates of point B'?

A: The coordinates of point B' are ${$ (6, -13)$}$.

Q: How were the coordinates of point B' calculated?

A: The coordinates of point B' were calculated by applying the translation rule to the pre-image coordinates of point B ${$ (4, -5)$}$.

Q: What does the translation of point B' indicate?

A: The translation of point B' indicates that point B has been moved 2 units to the right and 8 units down.