A line segment has endpoints at #(8 ,5 )# and #(2 ,1 )#. If the line segment is rotated about the origin by # pi #, translated horizontally by # - 1 #, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Jun 2, 2016
(8 ,5) → (9 ,-5) and (2 ,1) → (3 ,-1)
Explanation:
I am naming the endpoints A (8 ,5) and B (2 ,1) so we can follow what happens to each after each of the 3 transformations.
First transformation rotation about origin of
#pi# a point (x ,y) → (-x ,-y)
hence A (8 ,5) → A' (-8 ,-5) and B (2 ,1) → B'(-2 ,-1)
Second transformation Under a translation of
#((-1),(0))# a point (x ,y) → (x-1 ,y)
hence A' (-8 ,-5) → A''(-9 ,-5) and B' (-2 ,-1) →B'' (-3 ,-1)
Third transformation Reflection in the y-axis
a point (x ,y) → (-x ,y)
hence A'' (-9 ,-5) → (A''' (9 ,-5) and B'' (-3 ,-1) → B''' (3 ,-1)
Thus (8 ,5) → (9 ,-5) and (2 ,1) → (3 ,-1)
