A line segment has endpoints at #(7 ,5 )# and #(8 ,2 )#. If the line segment is rotated about the origin by # pi #, translated horizontally by # - 1 #, and reflected about the x-axis, what will the line segment's new endpoints be?

1 Answer
Jun 24, 2018

#(-8,5)" and "(-9,2)#

Explanation:

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

#A=(7,5)" and "B=(8,2)#

#color(blue)"first transformation"#

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

#• " a point "(x,y)to(-x,-y)#

#A(7,5)toA'(-7,-5)#

#B(8,2)toB'(-8,-2)#

#color(blue)"second transformation"#

#"under a horizontal translation "((-1),(0))#

#• " a point "(x,y)to(x-1,y)#

#A'(-7,-5)toA''(-8,-5)#

#B'(-8,-2)toB''(-9,-2)#

#color(blue)"third transformation"#

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

#• " a point " (x,y)to(x,-y)#

#A''(-8,-5)toA'''(-8,5)#

#B''(-9,-2)toB'''(-9,2)#

#"After all 3 transformations"#

#(7,5)to(-8,5)" and "(8,2)to(-9,2)#