IDNLearn.com is the perfect place to get answers, share knowledge, and learn new things. Join our platform to receive prompt and accurate responses from experienced professionals in various fields.
Sagot :
To determine the pre-image of the vertex [tex]\( A' \)[/tex] given the rule of reflection across the y-axis [tex]\( r_{\text{y-axis}}(x, y) \rightarrow (-x, y) \)[/tex]:
1. Understand the Reflection Rule: When reflecting a point across the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. Thus, for a point [tex]\((x, y)\)[/tex] under reflection, the image becomes [tex]\((-x, y)\)[/tex].
2. Identify the Given Image [tex]\( A' \)[/tex]:
Suppose the coordinates of the image vertex [tex]\( A' \)[/tex] are [tex]\( (4, 2) \)[/tex].
3. Use the Rule to Find Pre-image:
- According to [tex]\( r_{\text{y-axis}}(x, y) \rightarrow (-x, y) \)[/tex], given the image [tex]\( A' = (4, 2) \)[/tex]:
- Let the pre-image be [tex]\((x, y)\)[/tex]. For the point [tex]\((4, 2)\)[/tex] to be the reflected image, we reverse the sign change transformation:
[tex]\[ -x = 4 \implies x = -4 \][/tex]
The y-coordinate remains unchanged:
[tex]\[ y = 2 \][/tex]
4. Combine the Coordinates and Verify:
Thus, the pre-image [tex]\( A \)[/tex] is [tex]\((-4, 2)\)[/tex].
Therefore, the pre-image of the vertex [tex]\( A' \)[/tex] is [tex]\( \boxed{(-4, 2)} \)[/tex].
1. Understand the Reflection Rule: When reflecting a point across the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. Thus, for a point [tex]\((x, y)\)[/tex] under reflection, the image becomes [tex]\((-x, y)\)[/tex].
2. Identify the Given Image [tex]\( A' \)[/tex]:
Suppose the coordinates of the image vertex [tex]\( A' \)[/tex] are [tex]\( (4, 2) \)[/tex].
3. Use the Rule to Find Pre-image:
- According to [tex]\( r_{\text{y-axis}}(x, y) \rightarrow (-x, y) \)[/tex], given the image [tex]\( A' = (4, 2) \)[/tex]:
- Let the pre-image be [tex]\((x, y)\)[/tex]. For the point [tex]\((4, 2)\)[/tex] to be the reflected image, we reverse the sign change transformation:
[tex]\[ -x = 4 \implies x = -4 \][/tex]
The y-coordinate remains unchanged:
[tex]\[ y = 2 \][/tex]
4. Combine the Coordinates and Verify:
Thus, the pre-image [tex]\( A \)[/tex] is [tex]\((-4, 2)\)[/tex].
Therefore, the pre-image of the vertex [tex]\( A' \)[/tex] is [tex]\( \boxed{(-4, 2)} \)[/tex].
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your questions are important to us at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.