A line segment has endpoints at #(2 ,3 )# and #(8 ,9 )#. If the line segment is rotated about the origin by #( pi)/2 #, translated vertically by #-8 #, and reflected about the x-axis, what will the line segment's new endpoints be?

1 Answer
Jim G.
May 7, 2018

#(-3,6)" and "(-9,0)#

Explanation:

#"since there are 3 transformations to be performed"#
#"label the endpoints"#

#A(2,3)" and "B(8,9)#

#color(blue)"First transformation"#

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

#• " a point "(x,y)to(-y,x)#

#rArrA(2,3)toA'(-3,2)#

#rArrB(8,9)toB'(-9,8)#

#color(blue)"Second transformation"#

#"under a vertical translation "((0),(-8))#

#• " a point "(x,y)to(x,y-8)#

#rArrA'(-3,2)toA''(-3,-6)#

#rArrB'(-9,8)toB''(-9,0)#

#color(blue)"Third transformation"#

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

#• " a point "(x,y)to(x,-y)#

#rArrA''(-3,-6)toA'''(-3,6)#

#rArrB''(-9,0)toA'''(-9,0)#

#"After all 3 transformations"#

#(2,3)to(-3,6)" and "(8,9)to(-9,0)#

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