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?

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Answer 1 · 2018-02-03T15:55:44

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

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)#