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 vertically by # -4 #, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Dec 31, 2017
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"((0),(-4))#
#• " a point "(x,y)to(x,y-4)#
#rArrA'(2,-7)toA''(2,-11)#
#rArrB'(2,-3)toB''(2,-7)#
#color(blue)"third transformation"#
#"under a reflection in the y-axis"#
#• " a point "(x,y)to(-x,y)#
#rArrA''(2,-11)toA'''(-2,-11)#
#rArrB''(2,-7)toB'''(-2,-7)#
#"after all 3 transformations"#
#(7,2)to(-2,-11)" and "(3,2)to(-2,-7)#
