A line segment has endpoints at #(4 ,0 )# and #(2 ,1 )#. If the line segment is rotated about the origin by #( pi)/2 #, translated vertically by #-8 #, and reflected about the x-axis, what will the line segment's new endpoints be?
1 Answer
Dec 3, 2016
Explanation:
Since there are 3 transformations to be performed, label the endpoints A(4 ,0) and B(2 ,1)
First transformation Under a rotation about the origin of
#pi/2#
#"a point " (x,y)to(-y,x)# Hence A(4 ,0) → A'(0 ,4) and B(2 ,1) → B'(-1 ,2)
Second transformation Under a translation
#((0),(-8))#
#"a point " (x,y)to(x,y-8)# Hence A'(0 ,4) → A''(0 ,-4) and B'(-1 ,2) → B''(-1 ,-6)
Third transformation Under a reflection in the x-axis
#"a point " (x,y)to(x,-y)# Hence A''(0 ,-4) → A'''(0 ,4) and B''(-1 ,-6) → B'''(-1 ,6)
Thus after all 3 transformations.
#(4,0)to(0,4)" and " (2,1)to(-1,6)#
