A line segment has endpoints at #(9 ,4 )# and #(1 , 8 )#. 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
Jul 28, 2018
Explanation:
#"Since there are 3 transformations to be performed label"#
#"the endpoints"#
#A=(9,4)" and "B=(1,8)#
#color(blue)"first transformation"#
#"under a rotation about the origin of "pi/2#
#• " a point "(x,y)to(-y,x)#
#A(9,4)toA'(-4,9)#
#B(1,8)toB'(-8,1)#
#color(blue)"second transformation"#
#"under a horizontal translation "((5),(0))#
#• " a point "(x,y)to(x+5,y)#
#A'(-4,9)toA''(1,9)#
#B'(-8,1)toB''(-3,1)#
#color(blue)"third transformation"#
#"under a reflection in the y-axis"#
#• " a point "(x,y)to(-x,y)#
#A''(1,9)toA'''(-1,9)#
#B''(-3,1)toB'''(3,1)#
#"After all 3 transformations"#
#(9,4)to(-1,9)" and "(1,8)to(3,1)#
