Hexagon DEFGHI Is Translated 8 Units Down And 3 Units To The Right. If The Coordinates Of The Pre-image Of Point $F$ Are $(-9, 2)$, What Are The Coordinates Of $ F F F [/tex]?A. ( − 17 , 5 (-17, 5 ( − 17 , 5 ] B. $(-6,
Introduction
In geometry, coordinate translations are a fundamental concept that helps us understand how to move points from one location to another on a coordinate plane. When we translate a point, we are essentially moving it from one position to another without changing its size or shape. In this article, we will explore how to translate a hexagon and find the coordinates of a specific point after the translation.
What is a Coordinate Translation?
A coordinate translation is a transformation that moves a point from one location to another on a coordinate plane. It involves changing the coordinates of the point by adding or subtracting a certain value to the x-coordinate and/or the y-coordinate. In other words, we are shifting the point horizontally (left or right) and/or vertically (up or down) by a certain amount.
The Translation of Hexagon DEFGHI
In this problem, we are given a hexagon DEFGHI and asked to translate it 8 units down and 3 units to the right. This means that we need to add 3 to the x-coordinate and subtract 8 from the y-coordinate of each point on the hexagon.
The Pre-Image of Point F
The pre-image of point F is given as (-9, 2). This means that the original coordinates of point F are (-9, 2).
The Translation of Point F
To find the coordinates of point F after the translation, we need to add 3 to the x-coordinate and subtract 8 from the y-coordinate of the pre-image of point F. This can be calculated as follows:
x-coordinate: -9 + 3 = -6 y-coordinate: 2 - 8 = -6
Therefore, the coordinates of point F after the translation are (-6, -6).
Conclusion
In this article, we have explored the concept of coordinate translations in geometry and how to apply it to a specific problem. We have translated a hexagon 8 units down and 3 units to the right and found the coordinates of a specific point after the translation. By understanding coordinate translations, we can solve a wide range of problems in geometry and other areas of mathematics.
Discussion
- What is the difference between a translation and a rotation in geometry?
- How do you translate a point on a coordinate plane?
- What are some real-world applications of coordinate translations?
Answer Key
A. (-6, -6)
Additional Resources
- Khan Academy: Coordinate Geometry
- Math Open Reference: Coordinate Geometry
- Geometry Tutorials: Coordinate Geometry
Coordinate Translations Q&A =============================
Frequently Asked Questions
In this article, we will answer some of the most frequently asked questions about coordinate translations in geometry.
Q: What is the difference between a translation and a rotation in geometry?
A: A translation is a transformation that moves a point from one location to another on a coordinate plane without changing its size or shape. A rotation, on the other hand, is a transformation that turns a point around a fixed point (called the center of rotation) by a certain angle.
Q: How do you translate a point on a coordinate plane?
A: To translate a point on a coordinate plane, you need to add or subtract a certain value to the x-coordinate and/or the y-coordinate of the point. For example, if you want to translate a point 3 units to the right and 2 units up, you would add 3 to the x-coordinate and add 2 to the y-coordinate.
Q: What are some real-world applications of coordinate translations?
A: Coordinate translations have many real-world applications, including:
- Computer graphics: Coordinate translations are used to move objects on a screen and create animations.
- Video games: Coordinate translations are used to move characters and objects in a game.
- Architecture: Coordinate translations are used to design and build buildings and other structures.
- Engineering: Coordinate translations are used to design and build machines and other devices.
Q: How do you find the coordinates of a point after a translation?
A: To find the coordinates of a point after a translation, you need to add or subtract the translation values from the original coordinates of the point. For example, if the original coordinates of a point are (x, y) and the translation values are (h, k), the new coordinates of the point will be (x + h, y + k).
Q: What is the formula for translating a point on a coordinate plane?
A: The formula for translating a point on a coordinate plane is:
(x', y') = (x + h, y + k)
where (x, y) are the original coordinates of the point, (x', y') are the new coordinates of the point, and (h, k) are the translation values.
Q: Can you give an example of how to use the formula to translate a point?
A: Yes, here is an example:
Suppose we want to translate the point (2, 3) 4 units to the right and 2 units up. Using the formula, we get:
(x', y') = (2 + 4, 3 + 2) = (6, 5)
Therefore, the new coordinates of the point are (6, 5).
Conclusion
In this article, we have answered some of the most frequently asked questions about coordinate translations in geometry. We have discussed the difference between a translation and a rotation, how to translate a point on a coordinate plane, and some real-world applications of coordinate translations. We have also provided a formula for translating a point and given an example of how to use the formula.
Discussion
- What are some other types of transformations in geometry?
- How do you use coordinate translations to solve problems in geometry?
- What are some other real-world applications of coordinate translations?
Answer Key
- A translation is a transformation that moves a point from one location to another on a coordinate plane without changing its size or shape.
- To translate a point on a coordinate plane, you need to add or subtract a certain value to the x-coordinate and/or the y-coordinate of the point.
- Coordinate translations have many real-world applications, including computer graphics, video games, architecture, and engineering.
Additional Resources
- Khan Academy: Coordinate Geometry
- Math Open Reference: Coordinate Geometry
- Geometry Tutorials: Coordinate Geometry