A Triangle Is Drawn On The Coordinate Plane. It Is Translated 4 Units Right And 3 Units Down. Which Rule Describes The Translation?A. { (x, Y) \rightarrow (x+3, Y-4)$}$B. { (x, Y) \rightarrow (x+3, Y+4)$} C . \[ C. \[ C . \[ (x, Y)

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Introduction

In mathematics, particularly in geometry and coordinate geometry, understanding the concept of translation is crucial. Translation is a fundamental transformation that involves moving a figure from one position to another without changing its size or orientation. In this article, we will explore the concept of translation and apply it to a triangle drawn on the coordinate plane. We will examine the translation of the triangle 4 units right and 3 units down and determine the rule that describes this translation.

What is Translation?

Translation is a transformation that involves moving a figure from one position to another without changing its size or orientation. It is a rigid motion that preserves the shape and size of the figure. In the coordinate plane, translation can be represented by a vector, which is a mathematical object that has both magnitude and direction.

Translation Rules

There are several rules that describe translation in the coordinate plane. These rules involve changing the coordinates of the figure by adding or subtracting a certain value to the x-coordinate and/or the y-coordinate. The general rule for translation is:

{(x, y) \rightarrow (x + a, y + b)$}$

where (x, y) is the original point, (x + a, y + b) is the translated point, and (a, b) is the translation vector.

Applying Translation to a Triangle

Let's consider a triangle drawn on the coordinate plane. The triangle has vertices at (2, 3), (4, 5), and (6, 7). We want to translate this triangle 4 units right and 3 units down.

Step 1: Identify the Translation Vector

The translation vector is the vector that represents the movement of the triangle. In this case, the translation vector is (4, -3), since we are moving the triangle 4 units right and 3 units down.

Step 2: Apply the Translation Rule

To apply the translation rule, we need to add the translation vector to each vertex of the triangle. The new coordinates of the vertices will be:

  • (2 + 4, 3 - 3) = (6, 0)
  • (4 + 4, 5 - 3) = (8, 2)
  • (6 + 4, 7 - 3) = (10, 4)

Step 3: Determine the Translation Rule

Now that we have the new coordinates of the vertices, we can determine the translation rule that describes this translation. The translation rule is:

{(x, y) \rightarrow (x + 4, y - 3)$}$

This rule indicates that we need to add 4 to the x-coordinate and subtract 3 from the y-coordinate to translate the triangle 4 units right and 3 units down.

Conclusion

In conclusion, we have explored the concept of translation and applied it to a triangle drawn on the coordinate plane. We have determined the translation rule that describes the translation of the triangle 4 units right and 3 units down. The translation rule is:

{(x, y) \rightarrow (x + 4, y - 3)$}$

This rule can be used to translate any figure in the coordinate plane by adding 4 to the x-coordinate and subtracting 3 from the y-coordinate.

Discussion

Which of the following rules describes the translation of the triangle 4 units right and 3 units down?

A. {(x, y) \rightarrow (x+3, y-4)$}$ B. {(x, y) \rightarrow (x+3, y+4)$}$ C. {(x, y) \rightarrow (x+4, y-3)$}$

The correct answer is C. {(x, y) \rightarrow (x+4, y-3)$}$

Final Answer

The final answer is C.

Introduction

In our previous article, we explored the concept of translation and applied it to a triangle drawn on the coordinate plane. We determined the translation rule that describes the translation of the triangle 4 units right and 3 units down. In this article, we will provide a Q&A section to help clarify any doubts and provide additional information on the topic.

Q&A

Q1: What is the difference between translation and rotation?

A1: Translation is a transformation that involves moving a figure from one position to another without changing its size or orientation. Rotation, on the other hand, is a transformation that involves rotating a figure around a fixed point without changing its size or orientation.

Q2: How do I determine the translation vector?

A2: To determine the translation vector, you need to identify the direction and magnitude of the movement. In the case of the triangle, we moved it 4 units right and 3 units down, so the translation vector is (4, -3).

Q3: What is the general rule for translation?

A3: The general rule for translation is:

{(x, y) \rightarrow (x + a, y + b)$}$

where (x, y) is the original point, (x + a, y + b) is the translated point, and (a, b) is the translation vector.

Q4: How do I apply the translation rule to a figure?

A4: To apply the translation rule, you need to add the translation vector to each vertex of the figure. In the case of the triangle, we added the translation vector (4, -3) to each vertex to get the new coordinates.

Q5: What is the translation rule for the triangle 4 units right and 3 units down?

A5: The translation rule for the triangle 4 units right and 3 units down is:

{(x, y) \rightarrow (x + 4, y - 3)$}$

Q6: Can I use the translation rule to translate any figure?

A6: Yes, you can use the translation rule to translate any figure in the coordinate plane. The translation rule is a general rule that can be applied to any figure.

Q7: How do I determine the new coordinates of a figure after translation?

A7: To determine the new coordinates of a figure after translation, you need to add the translation vector to each vertex of the figure. In the case of the triangle, we added the translation vector (4, -3) to each vertex to get the new coordinates.

Q8: What is the difference between translation and reflection?

A8: Translation is a transformation that involves moving a figure from one position to another without changing its size or orientation. Reflection, on the other hand, is a transformation that involves flipping a figure over a fixed line without changing its size or orientation.

Conclusion

In conclusion, we have provided a Q&A section to help clarify any doubts and provide additional information on the topic of translation. We hope that this article has been helpful in understanding the concept of translation and how to apply it to figures in the coordinate plane.

Final Answer

The final answer is C.