If A Preimage Is At Points (0,1), (4,0), (4,1), What Are The Coordinates After A Translation Of 3 Units Up And Then A Reflection Over The Y-axis?A. (0,3), (4,3), (4,4)B. (3,0), (3,4), (-4,4)C. (0,4), (4,3), (4,4)D. (0,-1), (4,0), (4,-1)

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Introduction

In coordinate geometry, transformations play a crucial role in understanding the properties of shapes and figures. Two fundamental transformations are translation and reflection. In this article, we will explore the concept of translation and reflection, and how they can be applied to a given set of points.

Translation: Moving Points in a Coordinate Plane

A translation is a transformation that moves a point or a set of points from one location to another in a coordinate plane. The movement is done in a specific direction and by a certain distance. In this problem, we are given a set of points (0,1), (4,0), and (4,1) and asked to translate them 3 units up.

Translation of 3 Units Up

When we translate a point 3 units up, its y-coordinate increases by 3 units. The x-coordinate remains the same. Let's apply this translation to the given points:

  • (0,1) becomes (0,1+3) = (0,4)
  • (4,0) becomes (4,0+3) = (4,3)
  • (4,1) becomes (4,1+3) = (4,4)

So, after the translation of 3 units up, the new coordinates of the points are (0,4), (4,3), and (4,4).

Reflection over the Y-Axis

A reflection over the y-axis is a transformation that flips a point or a set of points over the y-axis. The x-coordinate changes sign, while the y-coordinate remains the same. In this problem, we are asked to reflect the translated points over the y-axis.

Reflection of the Translated Points

Let's apply the reflection over the y-axis to the translated points:

  • (0,4) becomes (0,-4) is incorrect, the correct answer is (0,4) remains the same because it is on the y-axis
  • (4,3) becomes (-4,3)
  • (4,4) becomes (-4,4)

So, after the reflection over the y-axis, the new coordinates of the points are (0,4), (-4,3), and (-4,4).

Conclusion

In this article, we have explored the concept of translation and reflection in coordinate geometry. We have applied these transformations to a given set of points and found the new coordinates after the translation of 3 units up and the reflection over the y-axis. The correct answer is (0,4), (-4,3), and (-4,4).

Answer

Introduction

In our previous article, we explored the concept of translation and reflection in coordinate geometry. We applied these transformations to a given set of points and found the new coordinates after the translation of 3 units up and the reflection over the y-axis. In this article, we will answer some frequently asked questions related to translation and reflection in coordinate geometry.

Q: What is the difference between translation and reflection?

A: Translation is a transformation that moves a point or a set of points from one location to another in a coordinate plane. The movement is done in a specific direction and by a certain distance. Reflection, on the other hand, is a transformation that flips a point or a set of points over a line or a point.

Q: How do I apply a translation to a point or a set of points?

A: To apply a translation to a point or a set of points, you need to add the translation distance to the x-coordinate and the y-coordinate of the point. For example, if you want to translate a point (2,3) 4 units to the right and 2 units up, the new coordinates of the point will be (2+4,3+2) = (6,5).

Q: How do I apply a reflection to a point or a set of points?

A: To apply a reflection to a point or a set of points, you need to change the sign of the x-coordinate and keep the y-coordinate the same. For example, if you want to reflect a point (2,3) over the y-axis, the new coordinates of the point will be (-2,3).

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 translation distance to the x-coordinate and the y-coordinate of the point.

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

A: A reflection changes the sign of the x-coordinate of a point and keeps the y-coordinate the same.

Q: Can I apply multiple transformations to a point or a set of points?

A: Yes, you can apply multiple transformations to a point or a set of points. The order in which you apply the transformations matters. For example, if you want to translate a point (2,3) 4 units to the right and then reflect it over the y-axis, the new coordinates of the point will be (6,3) and then (-6,3).

Q: How do I determine the type of transformation that has been applied to a point or a set of points?

A: To determine the type of transformation that has been applied to a point or a set of points, you need to look at the change in the coordinates of the point. If the x-coordinate has changed sign, it is a reflection. If the x-coordinate has increased or decreased by a certain distance, it is a translation.

Conclusion

In this article, we have answered some frequently asked questions related to translation and reflection in coordinate geometry. We have explained the difference between translation and reflection, how to apply these transformations to a point or a set of points, and how to determine the type of transformation that has been applied. We hope that this article has been helpful in understanding translation and reflection in coordinate geometry.

Frequently Asked Questions

  • Q: What is the difference between a translation and a reflection?
  • A: A translation is a transformation that moves a point or a set of points from one location to another in a coordinate plane. A reflection is a transformation that flips a point or a set of points over a line or a point.
  • Q: How do I apply a translation to a point or a set of points?
  • A: To apply a translation to a point or a set of points, you need to add the translation distance to the x-coordinate and the y-coordinate of the point.
  • Q: How do I apply a reflection to a point or a set of points?
  • A: To apply a reflection to a point or a set of points, you need to change the sign of the x-coordinate and keep the y-coordinate the same.

Glossary

  • Translation: A transformation that moves a point or a set of points from one location to another in a coordinate plane.
  • Reflection: A transformation that flips a point or a set of points over a line or a point.
  • Coordinate plane: A two-dimensional plane that is used to represent points and shapes.
  • X-coordinate: The horizontal coordinate of a point in a coordinate plane.
  • Y-coordinate: The vertical coordinate of a point in a coordinate plane.