A line segment has endpoints at #(2 , 1)# and #(7 ,6)#. If the line segment is rotated about the origin by #pi #, translated horizontally by #-3 #, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Jun 16, 2018
Explanation:
#"since there are 3 transformations to be performed label"#
#"the endpoints"#
#A=(2,1)" and "B=(7,6)#
#color(blue)"first transformation"#
#"under a rotation about the origin of "pi#
#• " a point "(x,y)to(-x,-y)#
#A(2,1)toA'(-2,-1)#
#B(7,6)toB'(-7,-6)#
#color(blue)"second transformation"#
#"under a horizontal translation "((-3),(0))#
#• " a point "(x,y)to(x-3,y)#
#A'(-2,-1)toA''(-5,-1)#
#B'(-7,-6)toB''(-10,-6)#
#color(blue)"third transformation"#
#"under a reflection in the y-axis"#
#• " a point "(x,y)to(-x,y)#
#A''(-5,-1)toA'''(5,-1)#
#B''(-10,-6)toB'''(10,-6)#
#"After all 3 transformations"#
#(2,1)to(5,-1)" and "(7,6)to(10,-6)#
