A line segment has endpoints at #(4 , 2)# and #(2 ,3)#. If the line segment is rotated about the origin by #(3pi)/2 #, translated horizontally by #7#, and reflected about the x-axis, what will the line segment's new endpoints be?

1 Answer
Jim G.
Jul 31, 2018

#(9,4)" and "(10,2)#

Explanation:

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

#A=(4,2)" and "B=(2,3)#

#color(blue)"first transformation"#

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

#• " a point "(x,y)to(y,-x)#

#A(4,2)toA'(2,-4)#

#B(2,3)toB'(3,-2)#

#color(blue)"second transformation"#

#"under a horizontal translation "((7),(0))#

#• " a point "(x,y)to(x+7,y)#

#A'(2,-4)toA''(9,-4)#

#B'(3,-2)toB''(10,-2)#

#color(blue)"third transformation"#

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

#• " a point "(x,y)to(x,-y)#

#A''(9,-4)toA'''(9,4)#

#B''(10,-2)toB'''(10,2)#

#"After all 3 transformations"#

#(4,2)to(9,4)" and "(2,3)to(10,2)#

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