# A line segment has endpoints at (3 ,7 ) and (5 ,9). If the line segment is rotated about the origin by (pi )/2 , translated vertically by 2 , and reflected about the y-axis, what will the line segment's new endpoints be?

New endpoints are $\left(9 , 7\right)$ and $\left(7 , 5\right)$

#### Explanation:

After rotating about the origin by $\frac{\pi}{2}$, the endpoints become
$\left(- 9 , 5\right)$ and $\left(- 7 , 3\right)$.

After translating vertically by 2, the endpoints become
$\left(- 9 , 7\right)$ and $\left(- 7 , 5\right)$.

Aftre reflecting about the y-axis, the final endpoints are
$\left(9 , 7\right)$ and $\left(7 , 5\right)$

God bless....I hope the explanation is useful.