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?

1 Answer
Roella W.
Feb 1, 2016

#(4.5,1.5)# and #(-2.5,1.5)#

Explanation:

Sketch
#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-(-2) = 7#. The point about which the line rotates is the midpoint of the line and is therefore #(1,(5-3.5)) = (1,1.5)#

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

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