A line segment has endpoints at #(3 , 2)# and #(1 ,3)#. If the line segment is rotated about the origin by #(3pi)/2 #, translated horizontally by #-5#, and reflected about the x-axis, what will the line segment's new endpoints be?
1 Answer
Dec 30, 2017
Explanation:
#"since there are 3 transformations to be performed label"#
#"the endpoints"#
#A(3,2)" and "B(1,3)#
#color(blue)"first transformation"#
#"under a rotation about the origin of "(3pi)/2#
#• " a point "(x,y)to(y,-x)#
#rArrA(3,2)toA'(2,-3)#
#rArrB(1,3)toB'(3,-1)#
#color(blue)"second transformation"#
#"under a translation " ((-5),(0))#
#• " a point "(x,y)to(x-5,y)#
#rArrA'(2,-3)toA''(-3,-3)#
#rArrB'(3,-1)toB''(-2,-1)#
#color(blue)"third transformation"#
#"under a reflection in the x-axis"#
#• " a point "(x,y)to(x,-y)#
#rArrA''(-3,-3)toA'''(-3,3)#
#rArrB''(-2,-1)toB'''(-2,1)#
#"under all 3 transformations"#
#(3,2)to(-3,3)" and "(1,3)to(-2,1)#
