A line segment has endpoints at #(7 , 4)# and #(2 , 5)#. If the line segment is rotated about the origin by #(3pi)/2 #, translated horizontally by #-3#, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Jul 19, 2018
Explanation:
#"Since there are 3 transformations to be performed label"#
#"the endpoints"#
#A=(7,4)" and "B=(2,5)#
#color(blue)"first transformation"#
#"under a rotation about the origin of "(3pi)/2#
#• " a point "(x,y)to(y,-x)#
#A(7,4)toA'(4,-7)#
#B(2,5)toB'(5,-2)#
#color(blue)"second transformation"#
#"under a horizontal translation "((-3),(0))#
#• " a point "(x,y)to(x-3,y)#
#A'(4,-7)toA''(1,-7)#
#B'(5,-2)toB''(2,-2)#
#color(blue)"third transformation"#
#"under a reflection in the y-axis"#
#• " a point "(x,y)to(-x,y)#
#A''(1,-7)toA'''(-1,-7)#
#B''(2,-2)toB'''(-2,-2)#
#"After all 3 transformations"#
#(7,4)to(-1,-7)" and "(2,5)to(-2,-2)#
