A line segment has endpoints at #(2 ,3 )# and #(6 ,5)#. If the line segment is rotated about the origin by #(3pi )/2 #, translated horizontally by #-1 #, and reflected about the x-axis, what will the line segment's new endpoints be?
1 Answer
Oct 3, 2016
Explanation:
Since there are 3 transformations to be performed here, name the endpoints A(2 ,3) and B(6 ,5), so that we can follow the changes that occur.
First transformation Under a rotation about the origin of
#(3pi)/2# a point (x ,y) → (y ,-x)
hence A(2 ,3) → A'(3 ,-2) and B(6 ,5) → B'(5 ,-6)
Second transformation Under a translation
#((-1),(0))# a point (x ,y) → (x-1 ,y+0) → (x-1 ,y)
hence A'(3 ,-2) → A''(2 ,-2) and B'(5 ,-6) → B''(4 ,-6)
Third transformation Under a reflection in the x-axis
a point (x ,y) → (x ,-y)
hence A''(2 ,-2) → A'''(2 ,2) and B''(4 ,-6) → B'''(4 ,6)
Thus after all 3 transformations.
#(2,3)to(2,2)" and " (6,5)to(4,6)#
