Question

If
𝐴
𝐵
‾

=
AB
=
15
15 inches then find the distance of
𝐴
′
𝐵
′
‾
A
′
B
′

after a reflection over the x-axis and a rotation of
119
°
119° clockwise.

Answer 1

To find the distance \( A'B' \) after reflecting \( AB \) over the x-axis and then rotating it 119° clockwise, we can follow these steps:

1. **Reflection over the x-axis:** Reflecting a point (x, y) over the x-axis transforms it to (x, -y). Thus, reflecting the segment \( AB \) does not change its length, it only changes its position in the coordinate system.

2. **Calculate distance \( AB \):** The original distance is given as \( AB = 15 \) inches.

3. **Rotation:** The rotation does not change the distance between points, it only changes their positions. Since the distance between two points remains constant under rotation, the distance after a rotation will still be equal to the original distance.

Thus, the distance \( A'B' \) after reflection and then rotation will also be \( 15 \) inches.

So, the final answer is:
\[
A'B' = 15 \text{ inches}
\]