# A line segment has endpoints at (7 ,6 ) and (5 ,1 ). If the line segment is rotated about the origin by  pi , translated horizontally by  - 4 , and reflected about the y-axis, what will the line segment's new endpoints be?

The new endpoints are $\left(11 , - 6\right)$ and $\left(9 , - 1\right)$
After the line segment has been rotated about the origin by $\pi$, the endpoints become $\left(- 7 , - 6\right)$ and $\left(- 5 , - 1\right)$. After translating horizontally by -4, the endpoints become $\left(- 9 , - 1\right)$ and $\left(- 11 , - 16\right)$. After reflecting the line segment about the y-axis, the final endpoints are $\left(9 , - 1\right)$ and $\left(11 , - 6\right)$