# A line segment with endpoints at (1 , -2 ) and (1, 8 ) is rotated clockwise by (3 pi)/2. What are the new endpoints of the line segment?

The new end points are
(-4,3) and (6,3)

#### Explanation:

The line joining $\left(1 , - 2\right) \mathmr{and} \left(1 , 8\right)$
forms a line parallel to y axis since x is same (1) for both the points

Let the line rotate with the line between the points as diameter.
The centre will be the mid point of the two points

$= \left(1 , \frac{- 2 + 8}{2}\right)$
$= - 1 , 3$

When the line rotates clockwise by$\frac{3 \pi}{2}$, about its mid point $\left(- 1 , 3\right)$ the y coordinate remains same as the centre.

Radius of rotation being distance from centre to its end point
from $\left(- 1 , 3\right)$ to $\left(1 , 8\right)$ which is $8 - 3 = 5$

x coordinate of $\left(1 , - 2\right)$ is reduced by $5 , t h u s 1 - 5 = - 4$
x coordinate of $\left(1 , 8\right)$ is increased by $5 , t h u s 1 + 5 = 6$

Now, (1,-2) has $b e c o m e \left(- 4 , 3\right)$

Also, (1,8) has  become (6,3)

Thus, the new end points are
(-4,3) and (6,3)