A line segment has endpoints at #(8 ,5 )# and #(2 ,1 )#. If the line segment is rotated about the origin by #( 3 pi)/2 #, translated horizontally by # - 1 #, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Feb 28, 2018
Explanation:
#"Since there are 3 transformations to be performed "#
#"label the endpoints"#
#A(8,5)" and "B(2,1)#
#color(blue)"First transformation"#
#"under a rotation about the origin of "(3pi)/2#
#• " a point "(x,y)to(y,-x)#
#rArrA(8,5)toA'(5,-8)#
#rArrB(2,1)toB'(1,-2)#
#color(blue)"Second transformation"#
#"under a translation "((-1),(0))#
#• " a point "(x,y)to(x-1,y)#
#rArrA'(5,-8)toA''(4,-8)#
#rArrB'(1,-2)toB''(0,-2)#
#color(blue)"Third transformation"#
#"under a reflection in the y-axis"#
#• " a point "(x,y)to(-x,y)#
#rArrA''(4,-8)toA'''(-4,-8)#
#rArrB''(0,-2)toB'''(0,-2)#
#"After all 3 transformations"#
#(8,5)to(-4,-8)" and "(2,1)to(0,-2)#
