A line segment has endpoints at #(7 ,9 )# and #(5 ,2)#. If the line segment is rotated about the origin by #pi #, translated vertically by #-4 #, and reflected about the x-axis, what will the line segment's new endpoints be?
1 Answer
Apr 7, 2017
Explanation:
Since there are 3 transformations to be performed, label the endpoints A(7 ,9) and B(5 ,2)
#color(blue)"first transformation" " Under a rotation about origin of " pi#
#"a point " (x,y)to(-x,-y)#
#"Hence "A(7,9)toA'(-7,-9)#
#"and " B(5,2)toB'(-5,-2)#
#color(blue)"Second transformation" " Under a translation " ((0),(-4))#
#"a point " (x,y)to(x,y-4)#
#"Hence " A'(-7,-9)toA''(-7,-13)#
#"and " B'(-5,-2)toB''(-5,-6)#
#color(blue)"third transformation"" Under a reflection in the x-axis"#
#"a point " (x,y)to(x,-y)#
#"Hence " A''(-7,-13)toA'''(-7,13)#
#"and " B''(-5,-6)toB'''(-5,6)#
#"After all 3 transformations"#
#(7,9)to(-7,13)" and " (5,2)to(-5,6)#
