# A line segment has endpoints at #(6 ,2 )# and #(3 ,7)#. If the line segment is rotated about the origin by #pi /2 #, translated vertically by #1 #, and reflected about the y-axis, what will the line segment's new endpoints be?

##### 1 Answer

May 25, 2018

#### Explanation:

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

#"the endpoints"#

#A(6,2)" and "B=(3,7)#

#color(blue)"first transformation"#

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

#• " a point "(x,y)to(-y,x)#

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

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

#color(blue)"second transformation"#

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

#• " a point "(x,y)to(x,y+1)#

#A'(-2,6)toA''(-2,7)#

#B'(-7,3)toB''(-7,4)#

#color(blue)"third transformation"#

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

#• " a point "(x,y)to(-x,y)#

#A''(-2,7)toA'''(2,7)#

#B''(-7,4)toB'''(7,4)#

#"After all 3 transformations"#

#(6,2)to(2,7)" and "(3,7)to(7,4)#