A line segment has endpoints at #(0 ,0 )# and #(1 , 3 )#. If the line segment is rotated about the origin by # pi /2 #, translated horizontally by # 5 #, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Jan 22, 2018
Explanation:
#"since there are 3 transformations to be performed"#
#"label the endpoints"#
#A(0,0)" and "B(1,3)#
#color(blue)"first transformation"#
#"under a rotation about the origin of "pi/2#
#• " a point "(x,y)to(-y,x)#
#rArrA(0,0)toA'(0,0)#
#rArrB(1,3)toB'(-3,1)#
#color(blue)"second transformation"#
#"under a translation "((5),(0))#
#• " a point "(x,y)to(x+5,y)#
#rArrA'(0,0)toA''(5,0)#
#rArrB'(-3,1)toB''(2,1)#
#color(blue)"third transformation"#
#"under a reflection in the y-axis"#
#• " a point "(x,y)to(-x,y)#
#rArrA''(5,0)toA'''(-5,0)#
#rArrB''(2,1)toB'''(-2,1)#
#"after all 3 transformations"#
#(0,0)to(-5,0)" and "(1,3)to(-2,1)#
