Finding an image under a given transformation

In summary, the conversation is discussing the limitations of using the equation y = b to represent a region transformation with the endpoint v = 1. The speaker believes this is not possible because v = 1 is a point, not a line segment, and the graph is bounded by a rectangle rather than being identical to it. They also mention that another graph is contained within the image of that rectangle.
  • #1
Miike012
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My question is in the paint document.
And I think I know the answer to my question. I asked why can't I let v = 1 then my first first region transformation would

the line y = b between -a≤x≤a.

The reason I think I can't do this is because the end point v = 1 is a point and not a line segment...
 

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  • #2
The graph is bounded by the rectangle ##|u|,|v|\le 1## but it isn't that rectangle. It is just contained in it. And the other graph is contained in the image of that rectangle, which is ##|x|\le a,|y|\le b##.
 

1. How do you find an image under a given transformation?

To find an image under a given transformation, you must first have a clear understanding of what the transformation is. This could be a translation, rotation, reflection, or dilation. Then, you can apply the transformation to each point or coordinate of the original image to determine the corresponding points of the transformed image.

2. What is the difference between pre-image and image?

The pre-image is the original shape or object before any transformation is applied. The image is the resulting shape or object after the transformation is applied to the pre-image.

3. How do you know if two images are congruent?

Two images are congruent if they have the same shape and size. To determine if two images are congruent, you can use various methods such as comparing their corresponding sides and angles, or using transformational geometry techniques to show that one image can be mapped onto the other with a series of transformations.

4. What is the importance of finding an image under a given transformation?

Finding an image under a given transformation is important in many fields of science and mathematics. It helps us understand the effects of transformations on shapes and objects, which is useful in areas such as computer graphics, engineering, and physics.

5. Are there any shortcuts or tricks for finding images under a given transformation?

There are some shortcuts and tricks that can be used to find images under certain transformations. For example, for translations, you can simply add or subtract the same value to each coordinate. For rotations and reflections, you can use patterns and symmetry to determine the coordinates of the transformed image. However, it is important to have a thorough understanding of the transformation to ensure accuracy and avoid mistakes.

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