# A line segment has endpoints at #(1 ,7 )# and #(3 ,1 )#. If the line segment is rotated about the origin by # pi #, translated horizontally by # - 4 #, and reflected about the y-axis, what will the line segment's new endpoints be?

##### 1 Answer

Jul 3, 2018

#### Explanation:

#"Since there are 3 transformations to be oerformed label"#

#"the endpoints"#

#A=(1,7)" and "B=(3,1)#

#color(blue)"first transformation"#

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

#• " a point "(x,y)to(-x,-y)#

#A(1,7)toA'(-1,-7)#

#B(3,1)toB'(-3,-1)#

#color(blue)"second transformation"#

#"under a horizontal translation "((-4),(0))#

#• " a point "(x,y)to(x-4,y)#

#A'(-1,-7)toA''(-5,-7)#

#B'(-3,-1)toB''(-7,-1)#

#color(blue)"third transformation"#

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

#• " a point "(x,y)to(-x,y)#

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

#B''(-7,-1)toB'''(7,-1)#

#"After all 3 transformations"#