A line segment has endpoints at #(4 ,2 )# and #(3 ,1 )#. 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
Jun 28, 2018
Explanation:
#"Since there are 3 transformations to be performed label"#
#"the endpoints"#
#A=(4,2)" and "B=(3,1)#
#color(blue)"first transformation"#
#"under a rotation about the origin of "pi/2#
#• " a point "(x,y)to(-y,x)#
#A(4,2)toA'(-2,4)#
#B(3,1)toB'(-1,3)#
#color(blue)"second transformation"#
#"under a vertical translation "((0),(1))#
#• " a point "(x,y)to(x,y+1)#
#A'(-2,4)toA''(-2,5)#
#B'(-1,3)toB''(-1,4)#
#color(blue)"third transformation"#
#"under a reflection in the y-axis"#
#• " a point "(x,y)to(-x,y)#
#A''(-2,5)toA'''(2,5)#
#B''(-1,4)toB'''(1,4)#
#"After all 3 transformations "#
#(4,2)to(2,5)" and "(3,1)to(1,4)#
