A line segment has endpoints at #(7 ,4 )# and #(5 ,2)#. If the line segment is rotated about the origin by #(3pi )/2 #, translated vertically by #5 #, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Feb 22, 2018
Explanation:
#"since there are 3 transformations to be performed label"#
#"the endpoints"#
#A(7,4)" and "B(5,2)#
#color(blue)"First transformation"#
#"under a rotation about the origin of "(3pi)/2#
#• " a point "(x,y)to(y,-x)#
#rArrA(7,4)toA'(4,-7)#
#rArrB(5,2)toB'(2,-5)#
#color(blue)" Second transformation"#
#"under a translation "((0),(5))#
#• " a point "(x,y)to(x,y+5)#
#rArrA'(4,-7)toA''(4,-2)#
#rArrB'(2,-5)toB''(2,0)#
#color(blue)"Third transformation"#
#"under a reflection in the y-axis"#
#• " a point "(x,y)to(x,-y)#
#rArrA''(4,-2)toA'''(4,2)#
#rArrB''(2,0)toB'''(2,0)#
#"After all 3 transformations"#
#(7,4)to(4,2)" and "(5,2)to(2,0)#
