A line segment has endpoints at #(2 , 2)# and #(5 , 4)#. If the line segment is rotated about the origin by #(pi)/2 #, translated vertically by #3#, and reflected about the y-axis, what will the line segment's new endpoints be?

1 Answer
George C.
Mar 13, 2016

#(2, 5)# and #(4, 8)#

Explanation:

Rotation through #pi/2# about the origin maps #(a, b)# to #(-b, a)#

Vertical translation by #3# maps #(a, b)# to #(a, b+3)#

Reflection about the #y#-axis maps #(a, b)# to #(-a, b)#

Performing each of these in sequence:

#(a, b) -> (-b, a) -> (-b, a+3) -> (b, a+3)#

Hence:

#(2, 2) -> (2, 5)#

#(5, 4) -> (4, 8)#

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