# A line segment has endpoints at (3 ,4 ) and (2 ,5 ). If the line segment is rotated about the origin by  pi /2 , translated horizontally by  1 , and reflected about the x-axis, what will the line segment's new endpoints be?

The new end points are $\left(- 4 , - 2\right)$ and $\left(- 3 , - 3\right)$

#### Explanation:

After rotating the segment by $\frac{\pi}{2}$, the new location is at the 2nd quadrant with end points $\left(- 5 , 2\right)$ and $\left(- 4 , 3\right)$.

Translating it horizontally by 1 will place it at the end points $\left(- 4 , 2\right)$ and $\left(- 3 , 3\right)$.

Reflecting it about the x-axis, will place it at the 3rd and final quadrant at the end points $\left(- 4 , - 2\right)$ and $\left(- 3 , - 3\right)$.

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