A line segment has endpoints at #(7 ,4 )# and #(2 ,6)#. 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 2, 2018

#(4,4)" and "(6,-1)#

Explanation:

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

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

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

#color(blue)"Second transformation"#

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

#• " a point "(x,y)to(x,y+3)#

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

#rArrB'(6,-2)toB''(6,1)#

#color(blue)"Third transformation"#

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

#• " a point "(x,y)to(x,-y)#

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

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

#"after all 3 transformations"#

#(7,4)to(4,4)" and "(2,6)to(6,-1)#

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