A line segment has endpoints at #(2 ,0 )# and #(1 , 3 )#. If the line segment is rotated about the origin by # pi /2 #, translated horizontally by # 1 #, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Mar 14, 2018
Explanation:
#"Since there are 3 transformations to be performed"#
#"Label the endpoints "A(2,0)" 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(2,0)toA'(0,2)#
#rArrB(1,3)toB'(-3,1)#
#color(blue)"second transformation"#
#"under a horizontal translation "((1),(0))#
#• " a point "(x,y)to(x+1,y)#
#rArrA'(0,2)toA''(1,2)#
#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''(1,2)toA'''(-1,2)#
#rArrB''(-2,1)toB'''(2,1)#
#"After all 3 transformations"#
#(2,0)to(-1,2)" and "(1,3)to(2,1)#
