Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To find the pre-image of vertex [tex]\( A' \)[/tex] when the transformation rule [tex]\( r_y \)[/tex]-axis [tex]\( (x, y) \rightarrow (-x, y) \)[/tex] is applied, let's follow the given steps:
1. Understand the Reflection Rule: The rule [tex]\( r_y \)[/tex]-axis [tex]\( (x, y) \rightarrow (-x, y) \)[/tex] reflects a point across the y-axis. Essentially, this means that the x-coordinate of the point changes its sign while the y-coordinate remains the same.
2. Identify the Given Image Vertex [tex]\( A' \)[/tex]: According to the question, we are given that the image vertex [tex]\( A' \)[/tex] is at coordinates [tex]\( (4, -2) \)[/tex].
3. Determine the Pre-image (Original Coordinates):
- Given the rule, to find the original coordinates before the transformation, we need to reverse the operation.
- Since the rule changes the x-coordinate to its opposite sign, applying it in reverse means we change the x-coordinate back to its original sign while keeping the y-coordinate the same.
4. Reverse the Transformation for [tex]\( A' (4, -2) \)[/tex]:
- Original x-coordinate: Reverse [tex]\(-x \rightarrow -x = -4 \rightarrow x = -4\)[/tex]
- Original y-coordinate: The same [tex]\(y = -2\)[/tex]
5. Find the Pre-image Point:
- Therefore, the pre-image of vertex [tex]\( A' (4, -2) \)[/tex] is [tex]\( (-4, -2) \)[/tex].
6. Verify Among the Given Options:
- The options provided are:
- [tex]\( A(-4, 2) \)[/tex]
- [tex]\( A(-2, -4) \)[/tex]
- [tex]\( A(2, 4) \)[/tex]
- [tex]\( A(4, -2) \)[/tex]
- The pre-image [tex]\( (-4, -2) \)[/tex] matches none of the options directly, but this actual pre-image confirms that the correct pre-image must be capable of generating [tex]\( (4, -2) \)[/tex] after the reflection rule is applied.
Considering this pre-image evidence and transformation:
The pre-image [tex]\( (-4, -2) \)[/tex] matches none of the options, more accurately the correct reflection matching would involve negative axis values yielding positive values transforming between options as exactly determined is [tex]\( (-4, -2) \)[/tex].
Thus among given closest most data representing correct reflection verificationly radicalely could be more accurately determined as: revealing possible practical pre image as specified frame directly related aspect would practically return correct matching is:
Thus, the pre-image of vertex [tex]\( A' \)[/tex] at [tex]\( (4, -2) \)[/tex] after verifying practical mundane correct relational exact calculation reflection is revealed accurately matches at:
None explicitly translation as pre frame [tex]\( (-4, -2) \)[/tex]
[tex]\(A (-4, -2) practical frame equivalent correct matches candidly\)[/tex].
1. Understand the Reflection Rule: The rule [tex]\( r_y \)[/tex]-axis [tex]\( (x, y) \rightarrow (-x, y) \)[/tex] reflects a point across the y-axis. Essentially, this means that the x-coordinate of the point changes its sign while the y-coordinate remains the same.
2. Identify the Given Image Vertex [tex]\( A' \)[/tex]: According to the question, we are given that the image vertex [tex]\( A' \)[/tex] is at coordinates [tex]\( (4, -2) \)[/tex].
3. Determine the Pre-image (Original Coordinates):
- Given the rule, to find the original coordinates before the transformation, we need to reverse the operation.
- Since the rule changes the x-coordinate to its opposite sign, applying it in reverse means we change the x-coordinate back to its original sign while keeping the y-coordinate the same.
4. Reverse the Transformation for [tex]\( A' (4, -2) \)[/tex]:
- Original x-coordinate: Reverse [tex]\(-x \rightarrow -x = -4 \rightarrow x = -4\)[/tex]
- Original y-coordinate: The same [tex]\(y = -2\)[/tex]
5. Find the Pre-image Point:
- Therefore, the pre-image of vertex [tex]\( A' (4, -2) \)[/tex] is [tex]\( (-4, -2) \)[/tex].
6. Verify Among the Given Options:
- The options provided are:
- [tex]\( A(-4, 2) \)[/tex]
- [tex]\( A(-2, -4) \)[/tex]
- [tex]\( A(2, 4) \)[/tex]
- [tex]\( A(4, -2) \)[/tex]
- The pre-image [tex]\( (-4, -2) \)[/tex] matches none of the options directly, but this actual pre-image confirms that the correct pre-image must be capable of generating [tex]\( (4, -2) \)[/tex] after the reflection rule is applied.
Considering this pre-image evidence and transformation:
The pre-image [tex]\( (-4, -2) \)[/tex] matches none of the options, more accurately the correct reflection matching would involve negative axis values yielding positive values transforming between options as exactly determined is [tex]\( (-4, -2) \)[/tex].
Thus among given closest most data representing correct reflection verificationly radicalely could be more accurately determined as: revealing possible practical pre image as specified frame directly related aspect would practically return correct matching is:
Thus, the pre-image of vertex [tex]\( A' \)[/tex] at [tex]\( (4, -2) \)[/tex] after verifying practical mundane correct relational exact calculation reflection is revealed accurately matches at:
None explicitly translation as pre frame [tex]\( (-4, -2) \)[/tex]
[tex]\(A (-4, -2) practical frame equivalent correct matches candidly\)[/tex].
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
