Point A(-3, 15) Undergoes A Translation Of 9 Units Right And 10 Units Down. What Are The Coordinates Of A'?

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Introduction

In mathematics, a translation is a fundamental concept that involves moving a point or an object from one location to another without changing its size or shape. This article will focus on a specific translation scenario where point A(-3, 15) undergoes a translation of 9 units right and 10 units down. We will explore the concept of translation, understand the given scenario, and determine the coordinates of point A' after the translation.

Understanding Translation

Translation is a type of transformation that involves moving a point or an object from one location to another. It is a rigid motion, meaning that the size and shape of the object remain unchanged during the translation. In a two-dimensional coordinate system, translation can be represented by adding or subtracting values to the x and y coordinates of a point.

The Given Scenario

In this scenario, point A(-3, 15) undergoes a translation of 9 units right and 10 units down. This means that the x-coordinate of point A will increase by 9 units, and the y-coordinate will decrease by 10 units.

Finding the Coordinates of A'

To find the coordinates of point A', we need to apply the translation to the original coordinates of point A. The new x-coordinate of A' will be the sum of the original x-coordinate and the translation value in the x-direction, which is 9 units. Similarly, the new y-coordinate of A' will be the difference between the original y-coordinate and the translation value in the y-direction, which is 10 units.

Calculating the Coordinates of A'

Let's calculate the coordinates of A' using the given translation values.

  • New x-coordinate of A' = Original x-coordinate of A + Translation value in x-direction = -3 + 9 = 6
  • New y-coordinate of A' = Original y-coordinate of A - Translation value in y-direction = 15 - 10 = 5

Therefore, the coordinates of point A' after the translation are (6, 5).

Conclusion

In this article, we explored the concept of translation and applied it to a specific scenario where point A(-3, 15) underwent a translation of 9 units right and 10 units down. We calculated the coordinates of point A' using the given translation values and determined that the new coordinates of A' are (6, 5). This article provides a clear understanding of the concept of translation and its application in mathematics.

Example Problems

  • Point B(4, 8) undergoes a translation of 5 units left and 3 units up. What are the coordinates of B'?
  • Point C(-2, 12) undergoes a translation of 8 units right and 6 units down. What are the coordinates of C'?

Solutions to Example Problems

  • Point B' = (4 - 5, 8 + 3) = (-1, 11)
  • Point C' = (-2 + 8, 12 - 6) = (6, 6)

Applications of Translation

Translation has numerous applications in various fields, including:

  • Computer graphics: Translation is used to move objects in a 2D or 3D space.
  • Engineering: Translation is used to design and analyze mechanical systems.
  • Architecture: Translation is used to design and plan buildings and structures.
  • Science: Translation is used to model and analyze physical systems.

Real-World Examples

  • A car moving from one location to another without changing its size or shape.
  • A plane flying from one airport to another without changing its size or shape.
  • A robot moving from one location to another without changing its size or shape.

Conclusion

In conclusion, translation is a fundamental concept in mathematics that involves moving a point or an object from one location to another without changing its size or shape. This article provided a clear understanding of the concept of translation and its application in mathematics. We calculated the coordinates of point A' after a translation of 9 units right and 10 units down and determined that the new coordinates of A' are (6, 5). This article also provided example problems and solutions to help readers understand the concept of translation.

Introduction

In our previous article, we explored the concept of translation and applied it to a specific scenario where point A(-3, 15) underwent a translation of 9 units right and 10 units down. We calculated the coordinates of point A' using the given translation values and determined that the new coordinates of A' are (6, 5). In this article, we will provide a Q&A section to help readers understand the concept of translation and its application in mathematics.

Q&A

Q1: What is translation in mathematics?

A1: Translation is a type of transformation that involves moving a point or an object from one location to another without changing its size or shape.

Q2: How do you represent translation in a two-dimensional coordinate system?

A2: Translation can be represented by adding or subtracting values to the x and y coordinates of a point.

Q3: What is the difference between translation and rotation?

A3: Translation involves moving a point or an object from one location to another without changing its size or shape, while rotation involves rotating a point or an object around a fixed point without changing its size or shape.

Q4: How do you calculate the coordinates of a point after a translation?

A4: To calculate the coordinates of a point after a translation, you need to add or subtract the translation values from the original coordinates of the point.

Q5: What are some real-world applications of translation?

A5: Translation has numerous applications in various fields, including computer graphics, engineering, architecture, and science.

Q6: Can you provide an example of a translation problem?

A6: Yes, here's an example: Point B(4, 8) undergoes a translation of 5 units left and 3 units up. What are the coordinates of B'? (Answer: (-1, 11))

Q7: How do you determine the direction of a translation?

A7: The direction of a translation can be determined by the signs of the translation values. If the translation value is positive, the point will move in the positive direction. If the translation value is negative, the point will move in the negative direction.

Q8: Can you provide an example of a translation problem with a negative translation value?

A8: Yes, here's an example: Point C(-2, 12) undergoes a translation of 8 units right and 6 units down. What are the coordinates of C'? (Answer: (6, 6))

Q9: How do you represent a translation in a 3D coordinate system?

A9: In a 3D coordinate system, translation can be represented by adding or subtracting values to the x, y, and z coordinates of a point.

Q10: Can you provide an example of a translation problem in a 3D coordinate system?

A10: Yes, here's an example: Point D(1, 2, 3) undergoes a translation of 4 units right, 5 units up, and 6 units forward. What are the coordinates of D'? (Answer: (5, 7, 9))

Conclusion

In this article, we provided a Q&A section to help readers understand the concept of translation and its application in mathematics. We answered questions on translation, its representation in a two-dimensional coordinate system, and its real-world applications. We also provided examples of translation problems and solutions to help readers understand the concept of translation.