A line segment has endpoints at #(2 ,1 )# and #(0 , 5 )#. If the line segment is rotated about the origin by # pi /2 #, translated horizontally by # 1 #, and reflected about the x-axis, what will the line segment's new endpoints be?

1 Answer
Apr 29, 2018

#(0,-2)" and "(-4,0)#

Explanation:

#"since there are 3 transformations to be performed label"#
#"the endpoints"#

#A(2,1)" and "B(0,5)#

#color(blue)"First transformation"#

#"under a rotation about the origin of "pi/2#

#• " a point "(x,y)to(-y,x)#

#rArrA(2,1)toA'(-1,2)#

#rArrB(0,5)toB'(-5,0)#

#color(blue)"Second transformation"#

#"under a translation "((1),(0))#

#• " a point "(x,y)to(x+1,y)#

#rArrA'(-1,2)toA''(0,2)#

#rArrB'(-5,0)toB''(-4,0)#

#color(blue)"Third transformation"#

#"under a reflection in the x-axis"#

#• " a point "(x,y)to(x,-y)#

#rArrA''(0,2)toA'''(0,-2)#

#rArrB''(-4,0)toB'''(-4,0)#

#"after all 3 transformations"#

#(2,1)to(0,-2)" and "(0,5)to(-4,0)#