# A line segment with endpoints at (1, 5) and (1, -2) is rotated clockwise by pi/2. What are the new endpoints of the line segment?

Feb 1, 2016

$\left(4.5 , 1.5\right)$ and $\left(- 2.5 , 1.5\right)$

#### Explanation:

$\frac{\pi}{2}$ is ${90}^{o}$ so the new position of the line is at right-angles to the old position which was vertical (constant $x$ value).

The length of the line is $5 - \left(- 2\right) = 7$. The point about which the line rotates is the midpoint of the line and is therefore $\left(1 , \left(5 - 3.5\right)\right) = \left(1 , 1.5\right)$

Because the line is now horizontal the new end points are $\left(\left(1 + 3.5\right) , 1.5\right)$ and $\left(\left(1 - 3.5\right) , 1.5\right)$ which are $\left(4.5 , 1.5\right)$ and $\left(- 2.5 , 1.5\right)$