A line segment has endpoints at #(3 , 4)# and #(1 ,9)#. If the line segment is rotated about the origin by #(3pi)/2 #, translated horizontally by #-2#, and reflected about the x-axis, what will the line segment's new endpoints be?
1 Answer
Apr 18, 2018
Explanation:
#"Since there are 3 transformations to be performed label"#
#"the endpoints"#
#A(3,4)" and "B(1,9)#
#color(blue)"First transformation"#
#"under a rotation about the origin of "(3pi)/2#
#• " a point "(x,y)to(y,-x)#
#rArrA(3,4)toA'(4,-3)#
#rArrB(1,9)toB'(9,-1)#
#color(blue)"Second transformation"#
#"under a translation "((-2),(0))#
#• " a point "(x,y)to(x-2,y)#
#rArrA'(4,-3)toA''(2,-3)#
#rArrB'(9,-1)toB''(7,-1)#
#color(blue)"Third transformation"#
#"under a reflection about the x-axis"#
#• " a point "(x,y)to(x,-y)#
#rArrA''(2,-3)toA'''(2,3)#
#rArrB''(7,-1)toB'''(7,1)#
#"After all 3 transformations"#
#(3,4)to(2,3)" and "(1,9)to(7,1)#
