A line segment has endpoints at #(7 ,4 )# and #(8 ,5 )#. If the line segment is rotated about the origin by #(3 pi)/2 #, translated vertically by #-2 #, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Feb 23, 2018
Explanation:
#"Since there are 3 transformations to be performed"#
#"label the endpoints"#
#A(7,4)" and "B(8,5)#
#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(8,5)toB'(5,-8)#
#color(blue)"Second transformation"#
#"under a translation "((0),(-2))#
#• " a point "(x,y)to(x,y-2)#
#rArrA'(4,-7)toA''(4,-9)#
#rArrB'(5,-8)toB''(5,-10)#
#color(blue)"Third transformation"#
#"under a reflection in the y-axis"#
#• " a point "(x,y)to(-x,y)#
#rArrA''(4,-9)toA'''(-4,-9)#
#rArrB''(5,-10)toB'''(-5,-10)#
#"After all 3 transformations"#
#(7,4)to(-4,-9)" and "(8,5)to(-5,-10)#
