A line segment has endpoints at #(3 ,7 )# and #(4 ,5)#. If the line segment is rotated about the origin by #(pi )/2 #, translated vertically by #-1 #, and reflected about the y-axis, what will the line segment's new endpoints be?

1 Answer
Jim G.
Jul 14, 2017

#(7,2)" and " (5,3)#

Explanation:

#"since there are 3 transformations to be performed"#

#"label the endpoints " A(3,7)" and " B(4,5)#

#color(blue)"First transformation"#

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

#• " a point "(x,y)to(-y,x)#

#rArrA(3,7)toA'(-7,3),B(4,5)toB'(-5,4)#

#color(blue)"Second transformation"#

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

#• " a point "(x,y)to(x,y-1)#

#rArrA'(-7,3)toA''(-7,2)#

#rArrB'(-5,4)toB''(-5,3)#

#color(blue)"Third transformation"#

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

#• " a point "(x,y)to(-x,y)#

#rArrA''(-7,2)toA'''(7,2)#

#rArrB''(-5,3)toB'''(5,3)#

#"after all 3 transformations"#

#(3,7)to(7,2)" and " (4,5)to(5,3)#

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