Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To find the coordinates of [tex]\( K' \)[/tex] after translating point [tex]\( K \)[/tex], we need to determine the translation vector that maps point [tex]\( J \)[/tex] to [tex]\( J' \)[/tex]. Here are the coordinates given:
- [tex]\( J(2, 4) \)[/tex]
- [tex]\( J'(3, 3) \)[/tex]
- [tex]\( K(3, 1) \)[/tex]
Step-by-Step Solution:
1. Determine the translation vector:
- The translation vector is calculated by finding the difference in the x-coordinates and y-coordinates of [tex]\( J \)[/tex] and [tex]\( J' \)[/tex]:
[tex]\[ \text{Translation vector} = (J'_x - J_x, J'_y - J_y) \][/tex]
- Substitute the given coordinates of [tex]\( J \)[/tex] and [tex]\( J' \)[/tex]:
[tex]\[ \text{Translation vector} = (3 - 2, 3 - 4) = (1, -1) \][/tex]
2. Apply the translation vector to point [tex]\( K \)[/tex]:
- To find the coordinates of [tex]\( K' \)[/tex], we add the components of the translation vector to the coordinates of [tex]\( K \)[/tex]:
[tex]\[ K'_x = K_x + 1 \][/tex]
[tex]\[ K'_y = K_y - 1 \][/tex]
- Substitute the given coordinates of [tex]\( K \)[/tex]:
[tex]\[ K'_x = 3 + 1 = 4 \][/tex]
[tex]\[ K'_y = 1 - 1 = 0 \][/tex]
3. Conclusion:
- Therefore, the coordinates of [tex]\( K' \)[/tex] are [tex]\((4, 0)\)[/tex].
So, the correct coordinates of [tex]\( K' \)[/tex] are [tex]\( \boxed{(4, 0)} \)[/tex].
- [tex]\( J(2, 4) \)[/tex]
- [tex]\( J'(3, 3) \)[/tex]
- [tex]\( K(3, 1) \)[/tex]
Step-by-Step Solution:
1. Determine the translation vector:
- The translation vector is calculated by finding the difference in the x-coordinates and y-coordinates of [tex]\( J \)[/tex] and [tex]\( J' \)[/tex]:
[tex]\[ \text{Translation vector} = (J'_x - J_x, J'_y - J_y) \][/tex]
- Substitute the given coordinates of [tex]\( J \)[/tex] and [tex]\( J' \)[/tex]:
[tex]\[ \text{Translation vector} = (3 - 2, 3 - 4) = (1, -1) \][/tex]
2. Apply the translation vector to point [tex]\( K \)[/tex]:
- To find the coordinates of [tex]\( K' \)[/tex], we add the components of the translation vector to the coordinates of [tex]\( K \)[/tex]:
[tex]\[ K'_x = K_x + 1 \][/tex]
[tex]\[ K'_y = K_y - 1 \][/tex]
- Substitute the given coordinates of [tex]\( K \)[/tex]:
[tex]\[ K'_x = 3 + 1 = 4 \][/tex]
[tex]\[ K'_y = 1 - 1 = 0 \][/tex]
3. Conclusion:
- Therefore, the coordinates of [tex]\( K' \)[/tex] are [tex]\((4, 0)\)[/tex].
So, the correct coordinates of [tex]\( K' \)[/tex] are [tex]\( \boxed{(4, 0)} \)[/tex].
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.