A line segment has endpoints at #(5 ,9 )# and #(8 ,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
Aug 20, 2016
Explanation:
Since there are 3 transformations to be performed here, name the endpoints A(5 , 9) and B(8 ,7) so that we can 'track' the points after each transformation.
First transformation Under a rotation about the origin of
#pi/2# a point (x ,y) → (-y ,x)
hence A(5 ,9) → A'(-9 ,5) and B(8 ,7) → B'(-7 ,8)
Second transformation Under a translation of
#((0),(-2))# a point (x ,y) → (x , y-2)
hence A'(-9 ,5) → A''(-9 ,3) and B'(-7 ,8) → B''(-7 ,6)
Third transformation Under a reflection in the y-axis
a point (x ,y) → (-x ,y)
hence A''(-9 ,3) → A'''(9 ,3) and B''(-7 ,6) → B'''(7 ,6)
Thus after all 3 transformations.
#(5,9)to(9,3)" and " (8,7)to(7,6)#
