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A line segment has endpoints at #(7 , 4)# and #(2 , 5)#. If the line segment is rotated about the origin by #(3pi)/2 #, translated horizontally by #-3#, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

James Atkins

#(-1,-7)" and "(-2,-2)#

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

#A=(7,4)" and "B=(2,5)#

#color(blue)"first transformation"#

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

#• " a point "(x,y)to(y,-x)#

#A(7,4)toA'(4,-7)#

#B(2,5)toB'(5,-2)#

#color(blue)"second transformation"#

#"under a horizontal translation "((-3),(0))#

#• " a point "(x,y)to(x-3,y)#

#A'(4,-7)toA''(1,-7)#

#B'(5,-2)toB''(2,-2)#

#color(blue)"third transformation"#

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

#• " a point "(x,y)to(-x,y)#

#A''(1,-7)toA'''(-1,-7)#

#B''(2,-2)toB'''(-2,-2)#

#"After all 3 transformations"#

#(7,4)to(-1,-7)" and "(2,5)to(-2,-2)#

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Answer 2

Carson Arnold

The line segment's new endpoints after the given transformations will be (-4, 7) and (-3, 2).

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