What Are The Coordinates Of The Reflection When $(4, -6)$ Is Reflected Across Both Axes?A. $(-4, 6)$B. $(4, 6)$C. $(6, 4)$D. $(4, 6)$

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Reflection Across Both Axes

When a point is reflected across both the x-axis and the y-axis, the x-coordinate and the y-coordinate are both negated. This is because the reflection across the x-axis changes the sign of the y-coordinate, and the reflection across the y-axis changes the sign of the x-coordinate.

Understanding the Reflection Process

To reflect a point across both axes, we need to follow these steps:

  1. Negate the x-coordinate: Change the sign of the x-coordinate by multiplying it by -1.
  2. Negate the y-coordinate: Change the sign of the y-coordinate by multiplying it by -1.

Applying the Reflection Process to the Given Point

Let's apply the reflection process to the point $(4, -6)$.

  1. Negate the x-coordinate: The x-coordinate is 4, so we multiply it by -1 to get -4.
  2. Negate the y-coordinate: The y-coordinate is -6, so we multiply it by -1 to get 6.

Calculating the Reflected Point

After applying the reflection process, we get the reflected point as $(-4, 6)$.

Conclusion

The coordinates of the reflection when $(4, -6)$ is reflected across both axes are $(-4, 6)$.

Answer

The correct answer is A. $(-4, 6)$.

Reflection Across One Axis

When a point is reflected across one axis, only the coordinate corresponding to that axis is negated.

Reflection Across the X-Axis

When a point is reflected across the x-axis, the y-coordinate is negated.

Reflection Across the Y-Axis

When a point is reflected across the y-axis, the x-coordinate is negated.

Understanding the Reflection Process Across One Axis

To reflect a point across one axis, we need to follow these steps:

  1. Negate the coordinate corresponding to the axis: Change the sign of the coordinate corresponding to the axis by multiplying it by -1.

Applying the Reflection Process Across One Axis to the Given Point

Let's apply the reflection process across one axis to the point $(4, -6)$.

Reflection Across the X-Axis

  1. Negate the y-coordinate: The y-coordinate is -6, so we multiply it by -1 to get 6.

The reflected point across the x-axis is $(4, 6)$.

Reflection Across the Y-Axis

  1. Negate the x-coordinate: The x-coordinate is 4, so we multiply it by -1 to get -4.

The reflected point across the y-axis is $(-4, -6)$.

Conclusion

The coordinates of the reflection when $(4, -6)$ is reflected across one axis are $(4, 6)$ and $(-4, -6)$.

Reflection Across Both Axes and One Axis

When a point is reflected across both axes and one axis, the coordinates are negated accordingly.

Reflection Across Both Axes and the X-Axis

When a point is reflected across both axes and the x-axis, the x-coordinate and the y-coordinate are both negated, and the y-coordinate is negated again.

Reflection Across Both Axes and the Y-Axis

When a point is reflected across both axes and the y-axis, the x-coordinate and the y-coordinate are both negated, and the x-coordinate is negated again.

Understanding the Reflection Process Across Both Axes and One Axis

To reflect a point across both axes and one axis, we need to follow these steps:

  1. Negate the x-coordinate: Change the sign of the x-coordinate by multiplying it by -1.
  2. Negate the y-coordinate: Change the sign of the y-coordinate by multiplying it by -1.
  3. Negate the coordinate corresponding to the axis: Change the sign of the coordinate corresponding to the axis by multiplying it by -1.

Applying the Reflection Process Across Both Axes and One Axis to the Given Point

Let's apply the reflection process across both axes and one axis to the point $(4, -6)$.

Reflection Across Both Axes and the X-Axis

  1. Negate the x-coordinate: The x-coordinate is 4, so we multiply it by -1 to get -4.
  2. Negate the y-coordinate: The y-coordinate is -6, so we multiply it by -1 to get 6.
  3. Negate the y-coordinate: The y-coordinate is 6, so we multiply it by -1 to get -6.

The reflected point across both axes and the x-axis is $(-4, -6)$.

Reflection Across Both Axes and the Y-Axis

  1. Negate the x-coordinate: The x-coordinate is 4, so we multiply it by -1 to get -4.
  2. Negate the y-coordinate: The y-coordinate is -6, so we multiply it by -1 to get 6.
  3. Negate the x-coordinate: The x-coordinate is -4, so we multiply it by -1 to get 4.

The reflected point across both axes and the y-axis is $(4, 6)$.

Conclusion

The coordinates of the reflection when $(4, -6)$ is reflected across both axes and one axis are $(-4, -6)$ and $(4, 6)$.

Reflection Across Both Axes and One Axis in 3D Space

When a point is reflected across both axes and one axis in 3D space, the coordinates are negated accordingly.

Reflection Across Both Axes and the X-Axis in 3D Space

When a point is reflected across both axes and the x-axis in 3D space, the x-coordinate and the y-coordinate and the z-coordinate are both negated, and the y-coordinate and the z-coordinate are negated again.

Reflection Across Both Axes and the Y-Axis in 3D Space

When a point is reflected across both axes and the y-axis in 3D space, the x-coordinate and the y-coordinate and the z-coordinate are both negated, and the x-coordinate and the z-coordinate are negated again.

Understanding the Reflection Process Across Both Axes and One Axis in 3D Space

To reflect a point across both axes and one axis in 3D space, we need to follow these steps:

  1. Negate the x-coordinate: Change the sign of the x-coordinate by multiplying it by -1.
  2. Negate the y-coordinate: Change the sign of the y-coordinate by multiplying it by -1.
  3. Negate the z-coordinate: Change the sign of the z-coordinate by multiplying it by -1.
  4. Negate the coordinate corresponding to the axis: Change the sign of the coordinate corresponding to the axis by multiplying it by -1.

Applying the Reflection Process Across Both Axes and One Axis in 3D Space to the Given Point

Let's apply the reflection process across both axes and one axis in 3D space to the point $(4, -6, 2)$.

Reflection Across Both Axes and the X-Axis in 3D Space

  1. Negate the x-coordinate: The x-coordinate is 4, so we multiply it by -1 to get -4.
  2. Negate the y-coordinate: The y-coordinate is -6, so we multiply it by -1 to get 6.
  3. Negate the z-coordinate: The z-coordinate is 2, so we multiply it by -1 to get -2.
  4. Negate the y-coordinate: The y-coordinate is 6, so we multiply it by -1 to get -6.

The reflected point across both axes and the x-axis in 3D space is $(-4, -6, -2)$.

Reflection Across Both Axes and the Y-Axis in 3D Space

  1. Negate the x-coordinate: The x-coordinate is 4, so we multiply it by -1 to get -4.
  2. Negate the y-coordinate: The y-coordinate is -6, so we multiply it by -1 to get 6.
  3. Negate the z-coordinate: The z-coordinate is 2, so we multiply it by -1 to get -2.
  4. Negate the x-coordinate: The x-coordinate is -4, so we multiply it by -1 to get 4.

The reflected point across both axes and the y-axis in 3D space is $(4, -6, -2)$.

Conclusion

The coordinates of the reflection when $(4, -6, 2)$ is reflected across both axes and one axis in 3D space are $(-4, -6, -2)$ and $(4, -6, -2)$.

Reflection Across Both Axes and One Axis in 4D Space

When a point is reflected across both axes and one axis in 4D space, the coordinates are negated accordingly.

Reflection Across Both Axes and the X-Axis in 4D Space

When a point is reflected across both axes and the x-axis in 4D space, the x-coordinate and the y-coordinate and the z-coordinate and the w-coordinate are both negated, and the y-coordinate and the z-coordinate and the w-coordinate are negated again.

Reflection Across Both Axes and the Y-Axis in 4D Space

When a point is reflected across both axes and the y-axis in 4D space, the x-coordinate and the y-coordinate and the z-coordinate and the w-coordinate

Q: What is reflection across axes?

A: Reflection across axes is a process of changing the sign of the coordinates of a point with respect to one or more axes. This is a fundamental concept in geometry and is used to describe the transformation of a point or a shape.

Q: What are the types of reflection across axes?

A: There are two main types of reflection across axes:

  1. Reflection across both axes: This involves changing the sign of both the x-coordinate and the y-coordinate.
  2. Reflection across one axis: This involves changing the sign of only one of the coordinates, either the x-coordinate or the y-coordinate.

Q: How do I reflect a point across both axes?

A: To reflect a point across both axes, you need to follow these steps:

  1. Negate the x-coordinate: Change the sign of the x-coordinate by multiplying it by -1.
  2. Negate the y-coordinate: Change the sign of the y-coordinate by multiplying it by -1.

Q: How do I reflect a point across one axis?

A: To reflect a point across one axis, you need to follow these steps:

  1. Negate the coordinate corresponding to the axis: Change the sign of the coordinate corresponding to the axis by multiplying it by -1.

Q: What is the effect of reflecting a point across both axes?

A: When a point is reflected across both axes, the x-coordinate and the y-coordinate are both negated, resulting in a new point with the coordinates changed.

Q: What is the effect of reflecting a point across one axis?

A: When a point is reflected across one axis, only the coordinate corresponding to that axis is negated, resulting in a new point with the coordinates changed.

Q: Can I reflect a point across both axes and one axis?

A: Yes, you can reflect a point across both axes and one axis. This involves changing the sign of both the x-coordinate and the y-coordinate, and then changing the sign of the coordinate corresponding to the axis.

Q: How do I reflect a point across both axes and one axis?

A: To reflect a point across both axes and one axis, you need to follow these steps:

  1. Negate the x-coordinate: Change the sign of the x-coordinate by multiplying it by -1.
  2. Negate the y-coordinate: Change the sign of the y-coordinate by multiplying it by -1.
  3. Negate the coordinate corresponding to the axis: Change the sign of the coordinate corresponding to the axis by multiplying it by -1.

Q: Can I reflect a point across both axes and one axis in 3D space?

A: Yes, you can reflect a point across both axes and one axis in 3D space. This involves changing the sign of the x-coordinate, the y-coordinate, and the z-coordinate, and then changing the sign of the coordinate corresponding to the axis.

Q: How do I reflect a point across both axes and one axis in 3D space?

A: To reflect a point across both axes and one axis in 3D space, you need to follow these steps:

  1. Negate the x-coordinate: Change the sign of the x-coordinate by multiplying it by -1.
  2. Negate the y-coordinate: Change the sign of the y-coordinate by multiplying it by -1.
  3. Negate the z-coordinate: Change the sign of the z-coordinate by multiplying it by -1.
  4. Negate the coordinate corresponding to the axis: Change the sign of the coordinate corresponding to the axis by multiplying it by -1.

Q: Can I reflect a point across both axes and one axis in 4D space?

A: Yes, you can reflect a point across both axes and one axis in 4D space. This involves changing the sign of the x-coordinate, the y-coordinate, the z-coordinate, and the w-coordinate, and then changing the sign of the coordinate corresponding to the axis.

Q: How do I reflect a point across both axes and one axis in 4D space?

A: To reflect a point across both axes and one axis in 4D space, you need to follow these steps:

  1. Negate the x-coordinate: Change the sign of the x-coordinate by multiplying it by -1.
  2. Negate the y-coordinate: Change the sign of the y-coordinate by multiplying it by -1.
  3. Negate the z-coordinate: Change the sign of the z-coordinate by multiplying it by -1.
  4. Negate the w-coordinate: Change the sign of the w-coordinate by multiplying it by -1.
  5. Negate the coordinate corresponding to the axis: Change the sign of the coordinate corresponding to the axis by multiplying it by -1.

Q: What are the applications of reflection across axes?

A: Reflection across axes has numerous applications in various fields, including:

  1. Geometry: Reflection across axes is used to describe the transformation of points and shapes.
  2. Computer Graphics: Reflection across axes is used to create 3D models and animations.
  3. Physics: Reflection across axes is used to describe the motion of objects.
  4. Engineering: Reflection across axes is used to design and analyze mechanical systems.

Q: What are the benefits of reflection across axes?

A: Reflection across axes has several benefits, including:

  1. Simplification of complex problems: Reflection across axes can simplify complex problems by breaking them down into smaller, more manageable parts.
  2. Improved understanding of geometric concepts: Reflection across axes can help improve understanding of geometric concepts, such as points, lines, and planes.
  3. Enhanced problem-solving skills: Reflection across axes can enhance problem-solving skills by providing a systematic approach to solving problems.

Q: What are the limitations of reflection across axes?

A: Reflection across axes has several limitations, including:

  1. Limited applicability: Reflection across axes is only applicable to points and shapes in 2D and 3D space.
  2. Difficulty in higher dimensions: Reflection across axes can be difficult to apply in higher dimensions, such as 4D space.
  3. Limited understanding of geometric concepts: Reflection across axes may not provide a complete understanding of geometric concepts, such as points, lines, and planes.