A line segment has endpoints at #(4 ,9 )# and #(2 ,7 )#. 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.
Jun 26, 2018

#(-9,4)" and "(-7,6)#

Explanation:

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

#A=(4,9)" and "B=(2,7)#

#color(blue)"first transformation"#

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

#• " a point "(x,y)to(-y,x)#

#A(4,9)toA'(-9,4)#

#B(2,7)toB'(-7,2)#

#color(blue)"second transformation"#

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

#• " a point "(x,y)to(x,y-8)#

#A'(-9,4)toA''(-9,-4)#

#B'(-7,2)toB''(-7,-6)#

#color(blue)"third transformation"#

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

#• " a point "(x,y)to(x,-y)#

#A''(-9,-4)toA'''(-9,4)#

#B''(-7,-6)toB'''(-7,6)#

#"After all 3 transformations"#

#(4,9)to(-9,4)" and "(2,7)to(-7,6)#

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