Join the growing community of curious minds on IDNLearn.com. Our platform provides detailed and accurate responses from experts, helping you navigate any topic with confidence.
Sagot :
Let's solve the problem step-by-step:
1. Initial Coordinates:
- Given points are [tex]\( A(3, 2) \)[/tex] and [tex]\( B(2, 3) \)[/tex].
2. Rotation by 180° about the Origin:
- When a point [tex]\((x, y)\)[/tex] is rotated 180° about the origin, its new coordinates become [tex]\((-x, -y)\)[/tex].
- For point [tex]\( A(3, 2) \)[/tex]:
- The new coordinates after rotation are [tex]\((-3, -2)\)[/tex].
- For point [tex]\( B(2, 3) \)[/tex]:
- The new coordinates after rotation are [tex]\((-2, -3)\)[/tex].
After the 180° rotation, the points are:
- [tex]\(A'(-3, -2)\)[/tex]
- [tex]\(B'(-2, -3)\)[/tex]
3. Reflection across the y-axis:
- When a point [tex]\((x, y)\)[/tex] is reflected across the y-axis, the x-coordinate is negated while the y-coordinate remains unchanged.
- For point [tex]\( A'(-3, -2) \)[/tex]:
- The new coordinates after reflection are [tex]\((3, -2)\)[/tex].
- For point [tex]\( B'(-2, -3) \)[/tex]:
- The new coordinates after reflection are [tex]\((2, -3)\)[/tex].
After reflection across the y-axis, the final points are:
- [tex]\(A''(3, -2)\)[/tex]
- [tex]\(B''(2, -3)\)[/tex]
Therefore, after rotating the line segment [tex]\( AB \)[/tex] about the origin through 180° and then reflecting it across the y-axis, the new coordinates of points A and B are [tex]\((3, -2)\)[/tex] and [tex]\((2, -3)\)[/tex] respectively.
1. Initial Coordinates:
- Given points are [tex]\( A(3, 2) \)[/tex] and [tex]\( B(2, 3) \)[/tex].
2. Rotation by 180° about the Origin:
- When a point [tex]\((x, y)\)[/tex] is rotated 180° about the origin, its new coordinates become [tex]\((-x, -y)\)[/tex].
- For point [tex]\( A(3, 2) \)[/tex]:
- The new coordinates after rotation are [tex]\((-3, -2)\)[/tex].
- For point [tex]\( B(2, 3) \)[/tex]:
- The new coordinates after rotation are [tex]\((-2, -3)\)[/tex].
After the 180° rotation, the points are:
- [tex]\(A'(-3, -2)\)[/tex]
- [tex]\(B'(-2, -3)\)[/tex]
3. Reflection across the y-axis:
- When a point [tex]\((x, y)\)[/tex] is reflected across the y-axis, the x-coordinate is negated while the y-coordinate remains unchanged.
- For point [tex]\( A'(-3, -2) \)[/tex]:
- The new coordinates after reflection are [tex]\((3, -2)\)[/tex].
- For point [tex]\( B'(-2, -3) \)[/tex]:
- The new coordinates after reflection are [tex]\((2, -3)\)[/tex].
After reflection across the y-axis, the final points are:
- [tex]\(A''(3, -2)\)[/tex]
- [tex]\(B''(2, -3)\)[/tex]
Therefore, after rotating the line segment [tex]\( AB \)[/tex] about the origin through 180° and then reflecting it across the y-axis, the new coordinates of points A and B are [tex]\((3, -2)\)[/tex] and [tex]\((2, -3)\)[/tex] respectively.
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Discover the answers you need at IDNLearn.com. Thank you for visiting, and we hope to see you again for more solutions.