A line segment has endpoints at #(2 ,0 )# and #(1 , 3 )#. If the line segment is rotated about the origin by # pi /2 #, translated horizontally by # 1 #, and reflected about the y-axis, what will the line segment's new endpoints be?

1 Answer
Jim G.
Mar 14, 2018

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

Explanation:

#"Since there are 3 transformations to be performed"#

#"Label the endpoints "A(2,0)" and "B(1,3)#

#color(blue)"first transformation"#

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

#• " a point "(x,y)to(-y,x)#

#rArrA(2,0)toA'(0,2)#

#rArrB(1,3)toB'(-3,1)#

#color(blue)"second transformation"#

#"under a horizontal translation "((1),(0))#

#• " a point "(x,y)to(x+1,y)#

#rArrA'(0,2)toA''(1,2)#

#rArrB'(-3,1)toB''(-2,1)#

#color(blue)"third transformation"#

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

#• " a point "(x,y)to(-x,y)#

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

#rArrB''(-2,1)toB'''(2,1)#

#"After all 3 transformations"#

#(2,0)to(-1,2)" and "(1,3)to(2,1)#

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