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
Jim G.
Jun 28, 2018

#(2,5)" and "(1,4)#

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)#

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