A line segment has endpoints at #(2 , 1)# and #(7 ,9)#. If the line segment is rotated about the origin by #pi #, translated horizontally by #4#, and reflected about the y-axis, what will the line segment's new endpoints be?

1 Answer
Jim G.
Aug 1, 2018

#(-2,-1)" and "(3,-9)#

Explanation:

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

#A=(2,1)" and "B=(7,9)#

#color(blue)"first transformation"#

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

#• " a point "(x,y)to(-x,-y)#

#A(2,1)toA'(-2,-1)#

#B(7,9)toB'(-7,-9)#

#color(blue)"second transformation"#

#"under a horizontal translation "((4),(0))#

#• " a point "(x,y)to(x+4,y)#

#A'(-2,-1)toA''(2,-1)#

#B'(-7,-9)toB''(-3,-9)#

#color(blue)"third transformation"#

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

#• " a point "(x,y)to(-x,y)#

#A''(2,-1)toA'''(-2,-1)#

#B''(-3,-9)toB'''(3,-9)#

#"After all 3 transformations"#

#(2,1)to(-2,-1)" and "(7,9)to(3,-9)#

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