A line segment has endpoints at #(1 ,2 )# and #(2 , 2 )#. If the line segment is rotated about the origin by #(3 pi ) /2 #, translated vertically by # -3 #, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Jul 27, 2018
Explanation:
#"Since there are 3 transformations to be performed label"#
#"the endpoints"#
#A=(1,2)" and "B=(2,2)#
#color(blue)"first transformation"#
#"under a rotation about the origin of "(3pi)/2#
#• " a point "(x,y)to(y,-x)#
#A(1,2)toA'(2,-1)#
#B(2,2)toB'(2,-2)#
#color(blue)"second transformation"#
#"under a vertical translation "((0),(-3))#
#• " a point "(x,y)to(x,y-3)#
#A'(2,-1)toA''(2,-4)#
#B'(2,-2)toB''(2,-5)#
#color(blue)"third transformation"#
#"under a reflection in the y-axis"#
#• " a point "(x,y)to(-x,y)#
#A''(2,-4)toA'''(-2,-4)#
#B''(2,-5)toB'''(-2,-5)#
#"After all 3 transformations"#
#(1,2)to(-2,-4)" and "(2,2)to(-2,-5)#
