A line segment has endpoints at #(9 ,1 )# and #(5 ,3)#. If the line segment is rotated about the origin by #pi #, translated vertically by #-1 #, and reflected about the x-axis, what will the line segment's new endpoints be?

1 Answer
Feb 27, 2018

#(-9,2)" and "(-5,4)#

Explanation:

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

#A(9,1)" and "B(5,3)#

#color(blue)"First transformation"#

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

#• " a point "(x,y)to(-x,-y)#

#rArrA(9,1)toA'(-9,-1)#

#rArrB(5,3)toB'(-5,-3)#

#color(blue)"Second transformation"#

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

#• " a point "(x,y)to(x,y-1)#

#rArrA'(-9,-1)toA''(-9,-2)#

#rArrB'(-5,-3)toB''(-5,-4)#

#color(blue)"Third transformation"#

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

#• " a point "(x,y)to(x,-y)#

#rArrA''(-9,-2)toA'''(-9,2)#

#rArrB''(-5,-4)toB'''(-5,4)#

#"After all 3 transformations"#

#(9,1)to(-9,2)" and "(5,3)to(-5,4)#