A line segment has endpoints at #(2 ,1 )# and #(7 , 3 )#. If the line segment is rotated about the origin by # pi /2 #, translated horizontally by # 1 #, and reflected about the x-axis, what will the line segment's new endpoints be?
1 Answer
Apr 26, 2018
Explanation:
#"Since there are 3 transformations to be oerformed label"#
#"the endpoints"#
#A(2,1)" and "B(7,3)#
#color(blue)"First transformation"#
#"under a rotation about the origin of "pi/2#
#• " a point "(x,y)to(-y,x)#
#rArrA(2,1)toA'(-1,2)#
#rArrB(7,3)toB'(-3,7)#
#color(blue)"Second transformation"#
#"under a translation "((1),(0))#
#• " a point "(x,y)to(x+1,y)#
#rArrA'(-1,2)toA''(0,2)#
#rArrB'(-3,7)toB''(-2,7)#
#color(blue)"Third transformation"#
#"under a reflection in the x-axis"#
#• " a point "(x,y)to(x,-y)#
#rArrA''(0,2)toA'''(0,-2)#
#rArrB''(-2,7)toB'''(-2,-7)#
#"After all 3 transformations"#
#(2,1)to(0,-2)" and "(7,3)to(-2,-7)#
