A line segment has endpoints at #(5 ,8 )# and #(7 ,6)#. If the line segment is rotated about the origin by #pi #, translated horizontally by #-3 #, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Aug 15, 2016
Explanation:
Since there are 3 transformations to be performed here, name the endpoints A(5 ,8) and B(7 ,6) so we can 'track' the coordinates after each transformation.
First transformation Under a rotation about origin of
#pi# a point (x ,y) → (-x ,-y)
hence A(5 ,8) → A'(-5 ,-8) and B(7 ,6) → B'(-7 ,-6)
Second transformation Under a translation of
#((-3),(0))# a point (x ,y) → (x-3 ,y)
hence A'(-5 ,-8) → A''(-8 ,-8) and B'(-7 ,-6) → B''(-10 ,-6)
Third transformation Under a reflection in the y-axis
a point (x ,y) → (-x ,y)
hence A''(-8 ,-8) → A'''(8 ,-8) and B''(-10 ,-6) → B'''(10 ,-6)
Thus after all 3 transformations.
#(5,8)to(8,-8)" and " (7,6)to(10,-6)#
