A line segment has endpoints at #(3 ,8 )# and #(4 ,6)#. If the line segment is rotated about the origin by #(pi )/2 #, translated vertically by #3 #, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Jan 2, 2017
Explanation:
Since there are 3 transformations to be performed here, label the endpoints A(3 ,8) and B(4 ,6)
First transformation Under a rotation about the origin of
#pi/2#
#"a point " (x,y)to(-y,x)# Hence A(3 ,8)→ A'(-8 ,3) and B(4 ,6) → B'(-6 ,4)
Second transformation Under a translation
#((0),(3))#
#"a point " (x,y)to(x,y+3)# Hence A'(-8 ,3) → A''(-8 ,6) and B'(-6 ,4) → B''(-6 ,7)
Third transformation Under a reflection in the y-axis
#"a point " (x,y)to(-x,y)# Hence A''(-8 ,6) → A'''(8 ,6) and B''(-6 ,7) → B'''(6 ,7)
After all 3 transformations.
#(3,8)to(8,6)" and " (4,6)to(6,7)#
