A line segment has endpoints at #(1 ,2 )# and #(3 ,8 )#. If the line segment is rotated about the origin by #pi /2 #, translated vertically by #1 #, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
May 16, 2018
Explanation:
#"since there are 3 transformations to be performed"#
#"label the endpoints"#
#A(1,2)" and "B(3,8)#
#color(blue)"First transformation"#
#"under a rotation about the origin of "pi/2#
#• " a point "(x,y)to(-y,x)#
#rArrA(1.2)toA'(-2,1)#
#rArrB(3,8)toB'*-8,3)#
#color(blue)"Second transformation"#
#"under a vertical translation "((0),(1))#
#•" a point "(x,y)to(x,y+1)#
#rArrA'(-2,1)toA''(-2,2)#
#rArrB'(-8,3)toB''(-8,4)#
#color(blue)"Third transformation"#
#"under a reflection in the y-axis"#
#• " a point "(x,y)to(-x,y)#
#rArrA''(-2,2)toA'''(2,2)#
#rArrB''(-8,4)toB'''(8,4)#
#"After all 3 transformations"#
#(1,2)to(2,2)" and "(3,8)to(8,4)#
