A line segment has endpoints at #(2 ,3 )# and #(2 ,1 )#. 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 9, 2018

#(-3,6)" and "(-1,6)#

Explanation:

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

#A=(2,3)" and "B=(2,1)#

#color(blue)"first transformation"#

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

#• " a point "(x,y)to(-y,x)#

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

#B(2,1)toB'(-1,2)#

#color(blue)"second transformation"#

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

#• " a point "(x,y)to(x,y-8)#

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

#B'(-1,2)toB''(-1,-6)#

#color(blue)"third transformation"#

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

#• " a point "(x,y)to(x,-y)#

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

#B''(-1,-6)toB'''(-1,6)#

#"After all 3 transformations"#

#(2,3)to(-3,6)" and "(2,1)to(-1,6)#

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