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
Jim G.
Jan 22, 2018

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

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)#

Related questions
See all questions in Rigid Transformations
Impact of this question
1395 views around the world
You can reuse this answer
Creative Commons License