A line segment has endpoints at #(3 ,1 )# and #(0 , 0 )#. If the line segment is rotated about the origin by # pi /2 #, translated horizontally by # 1 #, and reflected about the x-axis, what will the line segment's new endpoints be?
1 Answer
Jun 25, 2016
(3 ,1) → (0 ,-3) and (0 ,0) → (1 ,0)
Explanation:
Since there are 3 transformations to be performed, name the endpoints A(3 ,1) and B(0 ,0) so that we can 'track' them.
First transformation: Under a rotation about the origin of
#pi/2# a point (x ,y) → (-y ,x)
hence A(3 ,1) →A' (-1 ,3) and B(0 ,0) → B'(0 ,0)
Second transformation Under a translation
#((1),(0))# a point (x ,y) → (x+1 ,y)
hence A'(-1 ,3) → A''(0 ,3) and B'(0 ,0) → B''(1 ,0)
Third transformation Under a feflection in the x-axis
a point (x ,y) → (x ,-y)
hence A''(0 ,3) → A'''(0 ,-3) and B''(1 ,0) → B'''(1 ,0)
Thus (3 ,1) → (0 ,-3) and (0 ,0) → (1 ,0)
