A line segment has endpoints at #(1 ,2 )# and #(5 , 8 )#. If the line segment is rotated about the origin by #(3 pi ) /2 #, translated vertically by # -3 #, and reflected about the y-axis, what will the line segment's new endpoints be?

1 Answer
Jim G.
Aug 5, 2017

#(-2,-4)" and " (-8,-8)#

Explanation:

#"Since there are 3 transformations to be performed name the "#
#"endpoints A(1,2) and B(5,8)"#

#color(blue)"First transformation"#

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

#• " a point "(x,y)to(y,-x)#

#rArrA(1,2)toA'(2,-1)#

#rArrB(5,8)toB'(8,-5)#

#color(blue)"Second transformation"#

#"under a dilatation of "((0),(-3))#

#• " a point "(x,y)to(x,y-3)#

#rArrA'(2,-1)toA''(2,-4)#

#rArrB'(8,-5)toB''(8,-8)#

#color(blue)"Third transformation"#

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

#• " a point "(x,y)to(-x,y)#

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

#rArrB''(8,-8)toB'''(-8,-8)#

#"after all 3 transformations"#

#(1,2)to(-2,-4)" and "(5,8)to(-8,-8)#

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