A line segment has endpoints at #(3 , 4)# and #(2 , 6)#. If the line segment is rotated about the origin by #(3pi)/2 #, translated horizontally by #-2#, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
May 19, 2018
Explanation:
#"since there are 3 transformations to be performed label"#
#"the endpoints"#
#A=(3,4)" and "B=(2,6)#
#color(blue)"First transformation"#
#"under a rotation about the origin of "(3pi)/2#
#• " a point "(x,y)to(y,-x)#
#rArrA(3,4)toA'(4,-3)#
#rArrB(2,6)toB'(6,-2)#
#color(blue)"Second transformation"#
#"under a horizontal translation "((-2),(0))#
#• " a point "(x,y)to(x-2,y)#
#rArrA'(4,-3)toA''(2,-3)#
#rArrB'(6,-2)toB''(4,-2)#
#color(blue)"Third transformation"#
#"under a reflection in the y-axis"#
#• " a point "(x,y)to(-x,y)#
#rArrA''(2,-3)toA'''(-2,-3)#
#rArrB''(4,-2)toB'''(-4,-2)#
#"After all 3 transformations"#
#3,4)to(-2,-3)" and "(2,6)to(-4,-2)#
