Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To find the coordinates of the vertices of the pre-image trapezoid ABCD after applying the given transformation, let's follow these steps:
1. Understand the Transformations:
- Translation [tex]\( T_{4,0} \)[/tex] translates each point 4 units to the right.
- Reflection [tex]\( r_{y=x} \)[/tex] reflects each point over the line [tex]\( y = x \)[/tex].
2. Analyze the Given Points:
The coordinates provided are potential candidates for the pre-image vertices:
- [tex]\( (-1, 0) \)[/tex]
- [tex]\( (-1, -5) \)[/tex]
- [tex]\( (1, 1) \)[/tex]
- [tex]\( (7, 0) \)[/tex]
- [tex]\( (7, -5) \)[/tex]
3. Apply the Translation:
Applying the translation [tex]\( T_{4,0} \)[/tex] (4 units to the right):
- [tex]\( (-1, 0) \)[/tex] becomes [tex]\( (3, 0) \)[/tex]
- [tex]\( (-1, -5) \)[/tex] becomes [tex]\( (3, -5) \)[/tex]
- [tex]\( (1, 1) \)[/tex] becomes [tex]\( (5, 1) \)[/tex]
- [tex]\( (7, 0) \)[/tex] becomes [tex]\( (11, 0) \)[/tex]
- [tex]\( (7, -5) \)[/tex] becomes [tex]\( (11, -5) \)[/tex]
4. Apply the Reflection:
Applying the reflection [tex]\( r_{y=x} \)[/tex] (swapping x and y coordinates):
- [tex]\( (3, 0) \)[/tex] becomes [tex]\( (0, 3) \)[/tex]
- [tex]\( (3, -5) \)[/tex] becomes [tex]\( (-5, 3) \)[/tex]
- [tex]\( (5, 1) \)[/tex] becomes [tex]\( (1, 5) \)[/tex]
- [tex]\( (11, 0) \)[/tex] becomes [tex]\( (0, 11) \)[/tex]
- [tex]\( (11, -5) \)[/tex] becomes [tex]\( (-5, 11) \)[/tex]
5. Determine the Pre-Image Coordinates:
To determine which points are actually part of the pre-image (i.e., vertices of trapezoid ABCD before any transformation), check the resulting coordinates to see if they match:
- [tex]\( (0, 3) \)[/tex]
- [tex]\( (-5, 3) \)[/tex]
- [tex]\( (1, 5) \)[/tex]
- [tex]\( (0, 11) \)[/tex]
- [tex]\( (-5, 11) \)[/tex]
Since none of these coordinates appear to be among the given points, we conclude that after the transformations, these pre-image coordinates are not part of the original list of points mentioned.
Thus, upon careful consideration, it appears that none of the provided points are part of the vertices of the pre-image. The resulting list of pre-image vertices—taking into account the transformation steps—indicates no match with the given options.
The pre-image coordinates are indeterminable based on the options given after these sequences of transformations; hence, there are no correct choices among the provided coordinates.
1. Understand the Transformations:
- Translation [tex]\( T_{4,0} \)[/tex] translates each point 4 units to the right.
- Reflection [tex]\( r_{y=x} \)[/tex] reflects each point over the line [tex]\( y = x \)[/tex].
2. Analyze the Given Points:
The coordinates provided are potential candidates for the pre-image vertices:
- [tex]\( (-1, 0) \)[/tex]
- [tex]\( (-1, -5) \)[/tex]
- [tex]\( (1, 1) \)[/tex]
- [tex]\( (7, 0) \)[/tex]
- [tex]\( (7, -5) \)[/tex]
3. Apply the Translation:
Applying the translation [tex]\( T_{4,0} \)[/tex] (4 units to the right):
- [tex]\( (-1, 0) \)[/tex] becomes [tex]\( (3, 0) \)[/tex]
- [tex]\( (-1, -5) \)[/tex] becomes [tex]\( (3, -5) \)[/tex]
- [tex]\( (1, 1) \)[/tex] becomes [tex]\( (5, 1) \)[/tex]
- [tex]\( (7, 0) \)[/tex] becomes [tex]\( (11, 0) \)[/tex]
- [tex]\( (7, -5) \)[/tex] becomes [tex]\( (11, -5) \)[/tex]
4. Apply the Reflection:
Applying the reflection [tex]\( r_{y=x} \)[/tex] (swapping x and y coordinates):
- [tex]\( (3, 0) \)[/tex] becomes [tex]\( (0, 3) \)[/tex]
- [tex]\( (3, -5) \)[/tex] becomes [tex]\( (-5, 3) \)[/tex]
- [tex]\( (5, 1) \)[/tex] becomes [tex]\( (1, 5) \)[/tex]
- [tex]\( (11, 0) \)[/tex] becomes [tex]\( (0, 11) \)[/tex]
- [tex]\( (11, -5) \)[/tex] becomes [tex]\( (-5, 11) \)[/tex]
5. Determine the Pre-Image Coordinates:
To determine which points are actually part of the pre-image (i.e., vertices of trapezoid ABCD before any transformation), check the resulting coordinates to see if they match:
- [tex]\( (0, 3) \)[/tex]
- [tex]\( (-5, 3) \)[/tex]
- [tex]\( (1, 5) \)[/tex]
- [tex]\( (0, 11) \)[/tex]
- [tex]\( (-5, 11) \)[/tex]
Since none of these coordinates appear to be among the given points, we conclude that after the transformations, these pre-image coordinates are not part of the original list of points mentioned.
Thus, upon careful consideration, it appears that none of the provided points are part of the vertices of the pre-image. The resulting list of pre-image vertices—taking into account the transformation steps—indicates no match with the given options.
The pre-image coordinates are indeterminable based on the options given after these sequences of transformations; hence, there are no correct choices among the provided coordinates.
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
