At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To find the pre-image of vertex [tex]\( A' \)[/tex] under the given transformation rule [tex]\( r_y \)[/tex]-axis [tex]\((x, y) \rightarrow (-x, y) \)[/tex], we need to reverse this transformation. The transformation rule [tex]\( r_y \)[/tex]-axis reflects a point across the y-axis, changing the sign of its x-coordinate while keeping the y-coordinate the same. To find the original coordinates of the point before transformation, we need to apply the same reflection rule in reverse.
Given:
[tex]\( A' \)[/tex] has coordinates [tex]\( (2, 4) \)[/tex].
The rule is [tex]\((x, y) \rightarrow (-x, y)\)[/tex]. To reverse it, we will take the coordinates of [tex]\( A' \)[/tex] and change the sign of the x-coordinate back.
1. Start with [tex]\( A' = (2, 4) \)[/tex].
2. The x-coordinate of [tex]\( A \)[/tex] will be the opposite sign of the x-coordinate of [tex]\( A' \)[/tex]. Since the x-coordinate of [tex]\( A' \)[/tex] is 2, the x-coordinate of [tex]\( A \)[/tex] will be -2.
3. The y-coordinate remains the same. Therefore, the y-coordinate of [tex]\( A \)[/tex] will be 4.
Putting these together, the pre-image coordinates [tex]\( A \)[/tex] are:
[tex]\[ A = (-2, 4). \][/tex]
Therefore, the pre-image of vertex [tex]\( A' \)[/tex] is [tex]\( \boxed{(-2, 4)} \)[/tex].
Given:
[tex]\( A' \)[/tex] has coordinates [tex]\( (2, 4) \)[/tex].
The rule is [tex]\((x, y) \rightarrow (-x, y)\)[/tex]. To reverse it, we will take the coordinates of [tex]\( A' \)[/tex] and change the sign of the x-coordinate back.
1. Start with [tex]\( A' = (2, 4) \)[/tex].
2. The x-coordinate of [tex]\( A \)[/tex] will be the opposite sign of the x-coordinate of [tex]\( A' \)[/tex]. Since the x-coordinate of [tex]\( A' \)[/tex] is 2, the x-coordinate of [tex]\( A \)[/tex] will be -2.
3. The y-coordinate remains the same. Therefore, the y-coordinate of [tex]\( A \)[/tex] will be 4.
Putting these together, the pre-image coordinates [tex]\( A \)[/tex] are:
[tex]\[ A = (-2, 4). \][/tex]
Therefore, the pre-image of vertex [tex]\( A' \)[/tex] is [tex]\( \boxed{(-2, 4)} \)[/tex].
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.