A line segment has endpoints at #(7 ,5 )# and #(6 ,5)#. If the line segment is rotated about the origin by #(3pi )/2 #, translated vertically by #3 #, and reflected about the x-axis, what will the line segment's new endpoints be?

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Jim G. Share
May 23, 2018

Answer:

#(5,4)" and "(5,3)#

Explanation:

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

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

#color(blue)"first transformation"#

#"under a rotation about the origin of "(3pi)/2#

#• " a point "(x,y)to(y,-x)#

#A(7,5)toA'(5,-7)#

#B(6,5)toB'(5,-6)#

#color(blue)"second transformation"#

#"under a vertical translation "((0),(3))#

#• " a point "(x,y)to(x,y+3)#

#A'(5,-7)toA''(5,-4)#

#B'(5,-6)toB''(5,-3)#

#color(blue)"third transformation"#

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

#• " a point "(x,y)to(x,-y)#

#A''(5,-4)toA'''(5,4)#

#B''(5,-3)toB'''(5,3)#

#"After all 3 transformations"#

#(7,5)to(5,4)" and "(6,5)to(5,3)#

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