A Triangle On A Coordinate Plane Is Translated According To The Rule $T_{-8,4}(x, Y$\]. Which Is Another Way To Write This Rule?A. $(x, Y) \rightarrow (x+4, Y-8$\]B. $(x, Y) \rightarrow (x-4, Y-8$\]C. $(x, Y) \rightarrow

Introduction to Coordinate Plane Translations

In mathematics, a translation is a fundamental concept that involves moving a point or a shape from one location to another without changing its size or orientation. When dealing with coordinate planes, translations are often represented using a specific notation. In this article, we will explore the concept of coordinate plane translations and learn how to write a translation rule in a different form.

What is a Translation Rule?

A translation rule is a mathematical expression that describes how to move a point or a shape from one location to another on a coordinate plane. It is typically represented in the form of $(x, y) \rightarrow (x + a, y + b)$, where $(x, y)$ is the original point, and $(x + a, y + b)$ is the new location after the translation.

Understanding the Translation Rule $T_{-8,4}(x, y)$

The given translation rule is $T_{-8,4}(x, y)$. This rule indicates that the point $(x, y)$ is translated to a new location by moving it $-8$ units horizontally and $4$ units vertically. To understand this rule, let's break it down:

• The $-8$ in the subscript indicates that the point is moved $8$ units to the left (since it's negative).
• The $4$ in the subscript indicates that the point is moved $4$ units up (since it's positive).

Rewriting the Translation Rule

Now, let's rewrite the translation rule in a different form. We want to find another way to write the rule $T_{-8,4}(x, y)$. To do this, we need to understand the effect of the translation on the coordinates of the point.

• When the point is moved $-8$ units horizontally, its x-coordinate changes from $x$ to $x - 8$.
• When the point is moved $4$ units vertically, its y-coordinate changes from $y$ to $y + 4$.

Finding the Correct Answer

Based on the above analysis, we can rewrite the translation rule as $(x, y) \rightarrow (x - 8, y + 4)$. This is the correct answer.

Comparing with the Options

Let's compare our answer with the options provided:

A. $(x, y) \rightarrow (x + 4, y - 8)$ B. $(x, y) \rightarrow (x - 4, y - 8)$ C. $(x, y) \rightarrow (x - 8, y + 4)$

Our answer matches option C, which is the correct way to write the translation rule $T_{-8,4}(x, y)$.

Conclusion

In conclusion, we have learned how to rewrite a translation rule in a different form. By understanding the effect of the translation on the coordinates of the point, we can rewrite the rule as $(x, y) \rightarrow (x - 8, y + 4)$. This is an essential concept in mathematics, particularly in geometry and coordinate plane transformations.

Frequently Asked Questions

• Q: What is a translation rule? A: A translation rule is a mathematical expression that describes how to move a point or a shape from one location to another on a coordinate plane.
• Q: How do I rewrite a translation rule? A: To rewrite a translation rule, you need to understand the effect of the translation on the coordinates of the point.
• Q: What is the correct answer for the translation rule $T_{-8,4}(x, y)$? A: The correct answer is $(x, y) \rightarrow (x - 8, y + 4)$.

Further Reading

• Coordinate Plane Transformations
• Geometry and Coordinate Plane
• Translation Rules and Notations

References

• [1] "Coordinate Plane Transformations" by Math Open Reference
• [2] "Geometry and Coordinate Plane" by Khan Academy
• [3] "Translation Rules and Notations" by Wolfram MathWorld
  

Introduction

In our previous article, we explored the concept of coordinate plane translations and learned how to rewrite a translation rule in a different form. In this article, we will continue to discuss the topic of coordinate plane translations and provide answers to some frequently asked questions.

Q&A Session

Q1: What is a translation in mathematics?

A: A translation is a fundamental concept in mathematics that involves moving a point or a shape from one location to another without changing its size or orientation.

Q2: How do I represent a translation on a coordinate plane?

A: A translation can be represented on a coordinate plane using a specific notation, such as $(x, y) \rightarrow (x + a, y + b)$, where $(x, y)$ is the original point, and $(x + a, y + b)$ is the new location after the translation.

Q3: What is the difference between a translation and a rotation?

A: A translation involves moving a point or a shape from one location to another without changing its size or orientation, whereas a rotation involves rotating a point or a shape around a fixed point without changing its size or orientation.

Q4: How do I find the new coordinates of a point after a translation?

A: To find the new coordinates of a point after a translation, you need to add the translation values to the original coordinates. For example, if the original coordinates are $(x, y)$ and the translation values are $(a, b)$, the new coordinates will be $(x + a, y + b)$.

Q5: Can a translation be represented as a matrix?

A: Yes, a translation can be represented as a matrix. The translation matrix is a 2x2 matrix of the form $\begin{bmatrix} 1 & a \\ 0 & 1 \end{bmatrix}$, where $a$ is the translation value.

Q6: How do I perform a translation on a triangle?

A: To perform a translation on a triangle, you need to apply the translation values to each vertex of the triangle. For example, if the translation values are $(a, b)$, the new coordinates of the vertices will be $(x_1 + a, y_1 + b)$, $(x_2 + a, y_2 + b)$, and $(x_3 + a, y_3 + b)$.

Q7: Can a translation be combined with other transformations?

A: Yes, a translation can be combined with other transformations, such as rotations and scalings. The order of the transformations is important, as it can affect the final result.

Q8: How do I represent a translation in a programming language?

A: The representation of a translation in a programming language depends on the language and the specific implementation. However, it is common to use a matrix or a vector to represent the translation values.

Conclusion

In conclusion, we have provided answers to some frequently asked questions about coordinate plane translations. We hope that this article has been helpful in clarifying the concept of translations and how to represent them on a coordinate plane.

Frequently Asked Questions

• Q: What is a translation in mathematics? A: A translation is a fundamental concept in mathematics that involves moving a point or a shape from one location to another without changing its size or orientation.
• Q: How do I represent a translation on a coordinate plane? A: A translation can be represented on a coordinate plane using a specific notation, such as $(x, y) \rightarrow (x + a, y + b)$, where $(x, y)$ is the original point, and $(x + a, y + b)$ is the new location after the translation.
• Q: Can a translation be represented as a matrix? A: Yes, a translation can be represented as a matrix. The translation matrix is a 2x2 matrix of the form $\begin{bmatrix} 1 & a \\ 0 & 1 \end{bmatrix}$, where $a$ is the translation value.

Further Reading

• Coordinate Plane Transformations
• Geometry and Coordinate Plane
• Translation Rules and Notations

References

• [1] "Coordinate Plane Transformations" by Math Open Reference
• [2] "Geometry and Coordinate Plane" by Khan Academy
• [3] "Translation Rules and Notations" by Wolfram MathWorld