A Rectangle On A Coordinate Plane Is Translated 5 Units Up And 3 Units To The Left. Which Rule Describes The Translation?A. { (x, Y) \rightarrow (x+5, Y-3)$}$B. { (x, Y) \rightarrow (x+5, Y+3)$} C . \[ C. \[ C . \[ (x, Y) \rightarrow (x-3,
Understanding Coordinate Translations
In mathematics, a translation is a transformation that moves a figure from one location to another without changing its size or orientation. When a point on a coordinate plane is translated, its coordinates change. The new coordinates can be determined by adding or subtracting a certain value to the original coordinates.
The Translation Rules
There are two main rules for translating points on a coordinate plane:
- Horizontal Translation: When a point is translated horizontally, its x-coordinate changes. If the point is moved to the right, the x-coordinate increases. If the point is moved to the left, the x-coordinate decreases.
- Vertical Translation: When a point is translated vertically, its y-coordinate changes. If the point is moved up, the y-coordinate increases. If the point is moved down, the y-coordinate decreases.
Applying the Translation Rules
To determine the translation rule that describes the movement of a rectangle 5 units up and 3 units to the left, we need to analyze the changes in the coordinates.
- Horizontal Translation: Since the rectangle is moved 3 units to the left, the x-coordinate decreases by 3. This means that the new x-coordinate is x - 3.
- Vertical Translation: Since the rectangle is moved 5 units up, the y-coordinate increases by 5. This means that the new y-coordinate is y + 5.
The Correct Translation Rule
Based on the analysis, the correct translation rule that describes the movement of the rectangle 5 units up and 3 units to the left is:
This rule indicates that the x-coordinate decreases by 3 and the y-coordinate increases by 5.
Conclusion
In conclusion, the translation rule that describes the movement of a rectangle 5 units up and 3 units to the left is:
This rule is based on the analysis of the changes in the coordinates and follows the rules for horizontal and vertical translations.
Discussion
- What is the difference between a translation and a rotation?
- How do you determine the new coordinates of a point after a translation?
- Can you give an example of a translation that involves both horizontal and vertical movement?
Answer Key
- A translation is a transformation that moves a figure from one location to another without changing its size or orientation. A rotation is a transformation that turns a figure around a fixed point.
- To determine the new coordinates of a point after a translation, you need to add or subtract a certain value to the original coordinates.
- Yes, you can give an example of a translation that involves both horizontal and vertical movement. For example, a point that is translated 4 units to the right and 2 units up.
Additional Resources
Related Topics
Understanding Coordinate Translations
In mathematics, a translation is a transformation that moves a figure from one location to another without changing its size or orientation. When a point on a coordinate plane is translated, its coordinates change. The new coordinates can be determined by adding or subtracting a certain value to the original coordinates.
The Translation Rules
There are two main rules for translating points on a coordinate plane:
- Horizontal Translation: When a point is translated horizontally, its x-coordinate changes. If the point is moved to the right, the x-coordinate increases. If the point is moved to the left, the x-coordinate decreases.
- Vertical Translation: When a point is translated vertically, its y-coordinate changes. If the point is moved up, the y-coordinate increases. If the point is moved down, the y-coordinate decreases.
Applying the Translation Rules
To determine the translation rule that describes the movement of a rectangle 5 units up and 3 units to the left, we need to analyze the changes in the coordinates.
- Horizontal Translation: Since the rectangle is moved 3 units to the left, the x-coordinate decreases by 3. This means that the new x-coordinate is x - 3.
- Vertical Translation: Since the rectangle is moved 5 units up, the y-coordinate increases by 5. This means that the new y-coordinate is y + 5.
The Correct Translation Rule
Based on the analysis, the correct translation rule that describes the movement of the rectangle 5 units up and 3 units to the left is:
This rule indicates that the x-coordinate decreases by 3 and the y-coordinate increases by 5.
Q&A
Q: What is the difference between a translation and a rotation?
A: A translation is a transformation that moves a figure from one location to another without changing its size or orientation. A rotation is a transformation that turns a figure around a fixed point.
Q: How do you determine the new coordinates of a point after a translation?
A: To determine the new coordinates of a point after a translation, you need to add or subtract a certain value to the original coordinates.
Q: Can you give an example of a translation that involves both horizontal and vertical movement?
A: Yes, you can give an example of a translation that involves both horizontal and vertical movement. For example, a point that is translated 4 units to the right and 2 units up.
Q: What is the formula for a translation that moves a point 5 units up and 3 units to the left?
A: The formula for a translation that moves a point 5 units up and 3 units to the left is:
Q: How do you write a translation rule that moves a point 2 units down and 4 units to the right?
A: To write a translation rule that moves a point 2 units down and 4 units to the right, you need to subtract 2 from the y-coordinate and add 4 to the x-coordinate. The translation rule is:
Q: What is the difference between a translation and a reflection?
A: A translation is a transformation that moves a figure from one location to another without changing its size or orientation. A reflection is a transformation that flips a figure over a line without changing its size or orientation.
Q: Can you give an example of a translation that involves only horizontal movement?
A: Yes, you can give an example of a translation that involves only horizontal movement. For example, a point that is translated 6 units to the right.
Q: What is the formula for a translation that moves a point 3 units up and 2 units to the left?
A: The formula for a translation that moves a point 3 units up and 2 units to the left is:
Conclusion
In conclusion, the translation rule that describes the movement of a rectangle 5 units up and 3 units to the left is:
This rule is based on the analysis of the changes in the coordinates and follows the rules for horizontal and vertical translations.
Discussion
- What is the difference between a translation and a rotation?
- How do you determine the new coordinates of a point after a translation?
- Can you give an example of a translation that involves both horizontal and vertical movement?
Answer Key
- A translation is a transformation that moves a figure from one location to another without changing its size or orientation. A rotation is a transformation that turns a figure around a fixed point.
- To determine the new coordinates of a point after a translation, you need to add or subtract a certain value to the original coordinates.
- Yes, you can give an example of a translation that involves both horizontal and vertical movement. For example, a point that is translated 4 units to the right and 2 units up.