Answered

IDNLearn.com makes it easy to get reliable answers from experts and enthusiasts alike. Join our knowledgeable community and get detailed, reliable answers to all your questions.

The endpoints of the line segment AB are A (3, 2), and B (2, 3). If the line is rotated
about an origin through 180° in direction and reflected across y-axis, then find the
new coordinates of the line segment AB.
Note: Use your own words to answer this questio

Sagot :

GinnyAnsweridn
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.
We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Thank you for choosing IDNLearn.com. We’re committed to providing accurate answers, so visit us again soon.