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A line segment has endpoints at #(3 , 4)# and #(2 , 6)#. If the line segment is rotated about the origin by #(3pi)/2 #, translated horizontally by #-2#, and reflected about the y-axis, what will the line segment's new endpoints be?

1 Answer
May 19, 2018

Answer:

#(-2,-3)" and "(-4,-2)#

Explanation:

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

#A=(3,4)" and "B=(2,6)#

#color(blue)"First transformation"#

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

#• " a point "(x,y)to(y,-x)#

#rArrA(3,4)toA'(4,-3)#

#rArrB(2,6)toB'(6,-2)#

#color(blue)"Second transformation"#

#"under a horizontal translation "((-2),(0))#

#• " a point "(x,y)to(x-2,y)#

#rArrA'(4,-3)toA''(2,-3)#

#rArrB'(6,-2)toB''(4,-2)#

#color(blue)"Third transformation"#

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

#• " a point "(x,y)to(-x,y)#

#rArrA''(2,-3)toA'''(-2,-3)#

#rArrB''(4,-2)toB'''(-4,-2)#

#"After all 3 transformations"#

#3,4)to(-2,-3)" and "(2,6)to(-4,-2)#