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A line segment has endpoints at #(7 ,9 )# and #(3 ,6 )#. If the line segment is rotated about the origin by #(3 pi)/2 #, translated vertically by #4 #, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

Sophia Alfred

#(-9,-3)" and "(-6,1)#

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

#rArrA(7,9)" and "B(3,6)#

#color(blue)"First transformation"#

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

#• " a point "(x,y)to(y,-x)#

#rArrA(7,9)toA'(9,-7)#

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

#color(blue)"Second transformation"#

#"under a translation "((0),(4))#

#• " a point "(x,y)to(x,y+4)#

#rArrA'(9,-7)toA''(9,-3)#

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

#color(blue)"Third transformation"#

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

#• " a point "(x,y)to(-x,y)#

#rArrA''(9,-3)toA'''(-9,-3)#

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

#"after all 3 transformations"#

#(7,9)to(-9,-3)" and "(3,6)to(-6,1)#

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