A line segment has endpoints at #(7 ,4 )# and #(5 ,9)#. If the line segment is rotated about the origin by #(pi )/2 #, translated vertically by #5 #, and reflected about the y-axis, what will the line segment's new endpoints be?

1 Answer
Jim G.
Jun 7, 2017

#(-4,-2)" and " (-9,0)#

Explanation:

Since there are 3 transformations to be performed, label the endpoints.
#A(7,4)" and " B(5,9)#

#color(blue)"First transformation "#

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

#"a point " (x,y)to(-y,x)#

#rArrA(7,4)toA'(-4,7)" and " B(5,9)toB'(-9,5)#

#color(blue)"Second transformation"#

#"Under a translation of " ((0),(-5))#

#"a point " (x,y)to(x,y-5)#

#rArrA'(-4,7)toA''(-4,2)#

#"and " B'(-9,5)toB''(-9,0)#

#color(blue)"Third transformation"#

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

#"a point " (x,y)to(x,-y)#

#rArrA''(-4,2)toA'''(-4,-2)#

#"and " B''(-9,0)toB'''(-9,0)#

#"After all 3 transformations"#

#(7,4)to(-4,-2)" and " (5,9)to(-9,0)#

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