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