A line segment has endpoints at #(6 ,5 )# and #(5 ,7)#. If the line segment is rotated about the origin by #pi /2 #, translated vertically by #2 #, and reflected about the x-axis, what will the line segment's new endpoints be?

1 Answer
Jim G.
Jul 2, 2018

#(-5,-8)" and "(-7,-7)#

Explanation:

#"Since there are 3 transformations to be performed label"#
#"the endpoints"#

#A=(6,5)" and "B=(5,7)#

#color(blue)"first transformation"#

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

#• " a point "(x,y)to(-y,x)#

#A(6,5)toA'(-5,6)#

#B(5,7)toB'(-7,5)#

#color(blue)"second transformation"#

#"under a vertical translation "((0),(2))#

#• " a point "(x,y)to(x,y+2)#

#A'(-5,6)toA''(-5,8)#

#B'(-7,5)toB''(-7,7)#

#color(blue)"third transformation"#

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

#• " a point "(x,y)to(x,-y)#

#A''(-5,8)toA'''(-5,-8)#

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

#"After all 3 transformations"#

#(6,5)to(-5,-8)" and "(5,7)to(-7,-7)#

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