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
Jun 26, 2018
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)#
