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?

1 Answer

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

Explanation:

The line joining (1,-2) and (1,8)
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

=(1, (-2+8)/2)
=-1,3

When the line rotates clockwise by (3pi)/2, about its mid point (-1,3) the y coordinate remains same as the centre.

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

x coordinate of (1,-2) is reduced by 5, thus1 - 5 = -4
x coordinate of (1,8) is increased by 5, thus 1 + 5 = 6

Now, (1,-2) has become (-4,3)

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

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