A line segment has endpoints at #(7 ,5 )# and #(6 ,1)#. If the line segment is rotated about the origin by #(3pi )/2 #, translated vertically by #3 #, and reflected about the x-axis, what will the line segment's new endpoints be?

1 Answer
Jim G.
Feb 3, 2018

#(5,4)" and "(1,3)#

Explanation:

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

#A(7,5)" and "B(6,1)#

#color(blue)"First transformation"#

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

#• " a point "(x,y)to(y,-x)#

#rArrA(7,5)toA'(5,-7)#

#rArrB(6,1)toB'(1,-6)#

#color(blue)"Second transformation"#

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

#• " a point "(x,y)to(x,y+3)#

#rArrA'(5,-7)toA''(5,-4)#

#rArrB'(1,-6)toB''(1,-3)#

#color(blue)"Third transformation"#

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

#• " a point "(x,y)to(x,-y)#

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

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

#"after all 3 transformations"#

#(7,5)to(5,4)" and "6,1)to(1,3)#

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