You are given A''B''= T<4,2>(Ro 180(AB))

Given that A''(2,3) and is B"(-1,5), Where are the endpoints of AB located?
(what do i need to do to complete this problem?)

To determine the endpoints of AB, you need to find the coordinates of points A and B individually. Here's how you can do it step by step:

1. Start with the given information: A''(2,3) and B''(-1,5).

2. Apply the translation vector T<4,2> to each point A'' and B''. The translation vector represents a horizontal shift of 4 units to the right and a vertical shift of 2 units upward.

- For point A'': Add the translation vector T<4,2> to the coordinates of A'':
A' = (2 + 4, 3 + 2) = (6, 5)

- For point B'': Add the translation vector T<4,2> to the coordinates of B'':
B' = (-1 + 4, 5 + 2) = (3, 7)

3. Apply the rotation of 180° to the line segment AB.

To rotate a point (x, y) 180° around the origin, you can use the formula:
Ro180(x, y) = (-x, -y)

- For point A': Apply the rotation to A' coordinates:
A = Ro180(6, 5) = (-6, -5)

- For point B': Apply the rotation to B' coordinates:
B = Ro180(3, 7) = (-3, -7)

4. Now you have the coordinates of the endpoints A and B, which represent the original endpoints of AB after the translation and rotation.

- Point A: (-6, -5)
- Point B: (-3, -7)

Therefore, the endpoints of AB are A(-6, -5) and B(-3, -7).