# A line segment has endpoints at #(7 ,2 )# and #(3 , 2 )#. If the line segment is rotated about the origin by #(3 pi ) /2 #, translated horizontally by # 5 #, and reflected about the y-axis, what will the line segment's new endpoints be?

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Jim G.
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Feb 20, 2018

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#"since there are 3 transformations to be performed"#

#"label the endpoints"#

#A(7,2)" and "B(3,2)#

#color(blue)"First transformation"#

#"under a rotation about the origin of "(3pi)/2#

#• " a point "(x,y)to(y,-x)#

#rArrA(7,2)toA'(2,-7)#

#rArrB(3,2)toB'(2,-3)#

#color(blue)"Second transformation"#

#"under a translation "((5),(0))#

#• " a point "(x,y)to(x+5,y)#

#rArrA'(2,-7)toA''(7,-7)#

#rArrB'(2,-3)toB''(7,-3)#

#color(blue)"Third transformation"#

#"under a reflection in the y-axis"#

#• " a point "(x,y)to(-x,y)#

#rArrA''(7,-7)toA'''(-7,-7)#

#rArrB''(7,-3)toB'''(-7,-3)#

#"After all 3 transformations"#

#(7,2)to(-7,-7)" and "(3,2)to(-7,-3)#

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