A line segment has endpoints at #(6 ,2 )# and #(5 ,7)#. If the line segment is rotated about the origin by #pi /2 #, translated vertically by #2 #, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Jul 1, 2016
Explanation:
Since there are 3 transformation to be performed, name the endpoints A(6 ,2) and B(5 ,7) so that we can 'track' the changes after each transformation.
First transformation: Under a rotation about origin of
#pi/2# a point (x ,y) → (-y ,x)
hence A(6 ,2) → A'(-2 ,6) and B(5 ,7) → B'(-7 ,5)
Second transformation: Under a translation
#((0),(2))# a point (x ,y) → (x ,y+2)
hence A'(-2 ,6) → A''(-2 ,8) and B'(-7 ,5) → B''(-7 ,7)
Third transformation: Under a reflection in the y-axis
a point (x ,y) → (-x ,y)
hence A''(-2 ,8) → A'''(2 ,8) and B''(-7 ,7) → B'''(7 ,7)
Thus
#(6,2)to(2,8)" and " (5,7)to(7,7)#
