A line segment has endpoints at #(3 ,7 )# and #(4 ,9)#. 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
Oct 2, 2016
Explanation:
Since there are 3 transformations to be performed, name the endpoints A(3 ,7) and B(4 ,9) so that we can follow the changes that occur to them.
First transformation Under a rotation about the origin of
#pi/2# a point (x ,y) → (-y ,x)
hence A(3 ,7) → A'(-7 ,3) and B(4 ,9) → B'(-9 ,4)
Second transformation Under a translation
#((0),(2))# a point (x ,y) → (x+0 ,y+2) → (x ,y+2)
hence A'(-7 ,3) → A''(-7 ,5) and B'(-9 ,4) → B''(-9 ,6)
Third transformation Under a reflection in the y-axis
a point (x ,y) → (-x ,y)
hence A''(-7 ,5) → A'''(7 ,5) and B''(-9 ,6) → B'''(9 ,6)
Thus after all 3 transformations.
#(3,7)to(7,5)" and " (4,9)to(9,6)#
