A line segment has endpoints at #(3 ,5 )# and #(2 ,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
Aug 4, 2016
Explanation:
Since there are 3 transformations to be performed, name the endpoints A(3 ,5) and B(2 ,6) so that we can 'track' the points after each transformation.
First transformation Under a rotation about origin of
#pi/2# a point (x ,y) → (-x ,y)
hence A(3 ,5) → A'(-3 ,5) and B(2 ,6) → B'(-2 ,6)
Second transformation Under a translation
#((0),(3))# a point (x ,y) → (x ,y+3)
hence A'(-3 ,5) → A''(-3 ,8) and B'(-2 ,6) → B''(-2 ,9)
Third transformation Under a reflection in the y-axis
a point (x ,y) → (-x ,y)
hence A''(-3 ,8) → A'''(3 ,8) and B''(-2 ,9) → B'''(2 ,9)
Hence after all 3 transformations.
#(3,5)to(3,8)" and " (2,6)to(2,9)#
