A line segment has endpoints at #(2 ,6 )# and #(7 , 3 )#. If the line segment is rotated about the origin by # pi /2 #, translated horizontally by # 1 #, and reflected about the x-axis, what will the line segment's new endpoints be?

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Jim G. Share
Feb 26, 2018

Answer:

#(-5,-2)" and "(-2,-7)#

Explanation:

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

#A(2,6)" and "B(7,3)#

#color(blue)"First transformation"#

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

#• " a point "(x,y)to(-y,x)#

#rArrA(2,6)toA'(-6,2)#

#rArrB(7,3)toB'(-3,7)#

#color(blue)"Second transformation"#

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

#• " a point "(x,y)to(x+1,y)#

#rArrA'(-6,2)toA''(-5,2)#

#rArrB'(-3,7)toB''(-2,7)#

#color(blue)"Third transformation"#

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

#• " a point "(x,y)to(x,-y)#

#rArrA''(-5,2)toA'''(-5,-2)#

#rArrB''(-2,7)toB'''(-2,-7)#

#"After all 3 transformations"#

#(2,6)to(-5,-2)" and "(7,3)to(-2,-7)#

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