# A line segment has endpoints at (3 ,4 ) and (5 ,9). If the line segment is rotated about the origin by (pi )/2 , translated vertically by 3 , and reflected about the y-axis, what will the line segment's new endpoints be?

The new end points are (4,6) and (9,8)

#### Explanation:

Lets take each point individually
point (3,4)
after rotating by $\frac{\pi}{2}$ it becomes (-4,3)
translating it vertically by 3 makes it (-4,6)
reflected about y-axis it becomes (4,6)
point (5,9)
after rotating by $\frac{\pi}{2}$ it becomes (-9,5)
translating it vertically by 3 makes it (-9,8)
reflected about y-axis it becomes (9,8)

The new end points are (4,6) and (9,8)