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A line segment has endpoints at #(8 ,5 )# and #(2 ,1 )#. If the line segment is rotated about the origin by #( 3 pi)/2 #, translated horizontally by # - 1 #, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

Allison Allen

#(-4,-8)" and "(0,-2)#

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

#A(8,5)" and "B(2,1)#

#color(blue)"First transformation"#

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

#• " a point "(x,y)to(y,-x)#

#rArrA(8,5)toA'(5,-8)#

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

#color(blue)"Second transformation"#

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

#• " a point "(x,y)to(x-1,y)#

#rArrA'(5,-8)toA''(4,-8)#

#rArrB'(1,-2)toB''(0,-2)#

#color(blue)"Third transformation"#

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

#• " a point "(x,y)to(-x,y)#

#rArrA''(4,-8)toA'''(-4,-8)#

#rArrB''(0,-2)toB'''(0,-2)#

#"After all 3 transformations"#

#(8,5)to(-4,-8)" and "(2,1)to(0,-2)#

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Answer 2

Evelyn Arboleda

The new endpoints of the line segment after the described transformations are (-5, 2) and (-1, 8).

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