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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

Answer:

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

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)#