A line segment has endpoints at #(2 ,3 )# and #(8 ,9 )#. If the line segment is rotated about the origin by #( pi)/2 #, translated vertically by #-8 #, and reflected about the x-axis, what will the line segment's new endpoints be?
1 Answer
May 7, 2018
Explanation:
#"since there are 3 transformations to be performed"#
#"label the endpoints"#
#A(2,3)" and "B(8,9)#
#color(blue)"First transformation"#
#"under a rotation about the origin of "pi/2#
#• " a point "(x,y)to(-y,x)#
#rArrA(2,3)toA'(-3,2)#
#rArrB(8,9)toB'(-9,8)#
#color(blue)"Second transformation"#
#"under a vertical translation "((0),(-8))#
#• " a point "(x,y)to(x,y-8)#
#rArrA'(-3,2)toA''(-3,-6)#
#rArrB'(-9,8)toB''(-9,0)#
#color(blue)"Third transformation"#
#"under a reflection in the x-axis"#
#• " a point "(x,y)to(x,-y)#
#rArrA''(-3,-6)toA'''(-3,6)#
#rArrB''(-9,0)toA'''(-9,0)#
#"After all 3 transformations"#
#(2,3)to(-3,6)" and "(8,9)to(-9,0)#
