A line segment has endpoints at #(7 ,2 )# and #(3 , 2 )#. If the line segment is rotated about the origin by #(3 pi ) /2 #, translated horizontally by # 5 #, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Feb 20, 2018
Explanation:
#"since there are 3 transformations to be performed"#
#"label the endpoints"#
#A(7,2)" and "B(3,2)#
#color(blue)"First transformation"#
#"under a rotation about the origin of "(3pi)/2#
#• " a point "(x,y)to(y,-x)#
#rArrA(7,2)toA'(2,-7)#
#rArrB(3,2)toB'(2,-3)#
#color(blue)"Second transformation"#
#"under a translation "((5),(0))#
#• " a point "(x,y)to(x+5,y)#
#rArrA'(2,-7)toA''(7,-7)#
#rArrB'(2,-3)toB''(7,-3)#
#color(blue)"Third transformation"#
#"under a reflection in the y-axis"#
#• " a point "(x,y)to(-x,y)#
#rArrA''(7,-7)toA'''(-7,-7)#
#rArrB''(7,-3)toB'''(-7,-3)#
#"After all 3 transformations"#
#(7,2)to(-7,-7)" and "(3,2)to(-7,-3)#
