A line segment has endpoints at #(0 ,2 )# and #(3 ,5 )#. If the line segment is rotated about the origin by #( 3 pi)/2 #, translated vertically by # 3 #, and reflected about the x-axis, what will the line segment's new endpoints be?
1 Answer
Sep 12, 2016
Explanation:
Since there are 3 transformations to be performed here, name the endpoints A (0 ,2) and B (3 ,5) so that they may be 'tracked' after each transformation.
First transformation Under a rotation about the origin of
#(3pi)/2# a point (x ,y) → (y ,-x)
hence A(0 ,2) → A'(2 ,0) and B(3 ,5) → B'(5 ,-3)
Second transformation Under a translation
#((0),(3))# a point (x ,y) → (x ,y+3)
hence A'(2 ,0) → A''(2 ,3) and B'(5 ,-3) → B''(5 ,0)
Third transformation Under a reflection in the x-axis
a point (x ,y) → (x ,-y)
hence A''(2 ,3) → A'''(2 ,-3) and B''(5 ,0) → B'''(5 ,0)
Thus after all 3 transformations:
#(0,2)to(2,-3)" and " (3,5)to(5,0)#
