Hexagon DEFGHI Is Translated 8 Units Down And 3 Units To The Right. If The Coordinates Of The Pre-image Of Point F F F Are ( − 9 , 2 (-9, 2 ( − 9 , 2 ], What Are The Coordinates Of F ′ F^{\prime} F ′ ?A. ( − 17 , 5 (-17, 5 ( − 17 , 5 ] B. ( − 6 , − 6 (-6, -6 ( − 6 , − 6 ] C.

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Introduction

Transformations are a fundamental concept in geometry, and they play a crucial role in understanding various mathematical concepts. In this article, we will explore the concept of transformations, specifically the translation of a hexagon, and how it affects the coordinates of its points.

What is a Translation?

A translation is a type of transformation that involves moving a figure from one location to another without changing its size or shape. In other words, a translation is a rigid motion that preserves the distance and angle between points. The key characteristic of a translation is that it involves a change in position, but not a change in size or shape.

The Translation of Hexagon DEFGHI

In this problem, we are given a hexagon DEFGHI, which is translated 8 units down and 3 units to the right. This means that each point of the hexagon is moved 8 units down and 3 units to the right. We are also given the coordinates of the pre-image of point F, which are (-9, 2).

How to Find the Coordinates of F'

To find the coordinates of F', we need to apply the translation to the coordinates of F. Since the translation involves moving 8 units down and 3 units to the right, we can add 3 to the x-coordinate and subtract 8 from the y-coordinate of F.

Step 1: Identify the Coordinates of F

The coordinates of F are given as (-9, 2).

Step 2: Apply the Translation

To apply the translation, we add 3 to the x-coordinate and subtract 8 from the y-coordinate of F.

x-coordinate of F' = x-coordinate of F + 3 = -9 + 3 = -6

y-coordinate of F' = y-coordinate of F - 8 = 2 - 8 = -6

Conclusion

Therefore, the coordinates of F' are (-6, -6).

Answer

The correct answer is B. (-6, -6).

Discussion

This problem requires a good understanding of transformations, specifically translations. The key concept to understand is that a translation involves moving a figure from one location to another without changing its size or shape. By applying the translation to the coordinates of F, we can find the coordinates of F'.

Tips and Tricks

  • Make sure to understand the concept of translations and how they affect the coordinates of points.
  • Pay attention to the direction of the translation (up, down, left, or right).
  • Use the correct formula to apply the translation to the coordinates of a point.

Related Problems

  • Find the coordinates of the image of a point after a translation of 5 units up and 2 units to the left.
  • A triangle is translated 3 units down and 4 units to the right. Find the coordinates of the image of a point on the triangle.

Conclusion

Introduction

Transformations are a fundamental concept in geometry, and they play a crucial role in understanding various mathematical concepts. In our previous article, we explored the concept of transformations, specifically the translation of a hexagon, and how it affects the coordinates of its points. In this article, we will continue to explore transformations and answer some frequently asked questions.

Q&A

Q: What is a translation in geometry?

A: A translation is a type of transformation that involves moving a figure from one location to another without changing its size or shape. In other words, a translation is a rigid motion that preserves the distance and angle between points.

Q: How do I apply a translation to a point?

A: To apply a translation to a point, you need to add the horizontal component of the translation to the x-coordinate of the point and add the vertical component of the translation to the y-coordinate of the point.

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

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

Q: Can a translation be represented as a matrix?

A: Yes, a translation can be represented as a matrix. The matrix for a translation is of the form:

[1 0 x] [0 1 y] [0 0 1]

where (x, y) is the translation vector.

Q: How do I find the image of a point after a translation?

A: To find the image of a point after a translation, you need to apply the translation to the coordinates of the point. This involves adding the horizontal component of the translation to the x-coordinate of the point and adding the vertical component of the translation to the y-coordinate of the point.

Q: Can a translation be combined with other transformations?

A: Yes, a translation can be combined with other transformations such as rotations and reflections. However, the order in which the transformations are applied is important.

Q: What is the effect of a translation on the coordinates of a point?

A: A translation changes the coordinates of a point by adding the horizontal component of the translation to the x-coordinate and adding the vertical component of the translation to the y-coordinate.

Q: Can a translation be represented as a function?

A: Yes, a translation can be represented as a function. The function for a translation is of the form:

f(x, y) = (x + a, y + b)

where (a, b) is the translation vector.

Q: How do I find the inverse of a translation?

A: To find the inverse of a translation, you need to subtract the horizontal component of the translation from the x-coordinate and subtract the vertical component of the translation from the y-coordinate.

Conclusion

In conclusion, this article has provided answers to some frequently asked questions about transformations in geometry. We have explored the concept of translations and how they affect the coordinates of points. We have also discussed how translations can be represented as matrices and functions, and how they can be combined with other transformations.