A line segment has endpoints at #(7 ,2 )# and #(2 ,3 )#. If the line segment is rotated about the origin by # pi #, translated horizontally by # - 4 #, and reflected about the y-axis, what will the line segment's new endpoints be?
1 Answer
Aug 25, 2016
Explanation:
Since there are 3 transformations to be performed here, name the endpoints A(7 ,2) and B(2 ,3) so that we can 'track' the coordinates after each transformation.
First transformation Under a rotation about the origin of
#pi# a point (x ,y) → (-x ,-y)
hence A(7 ,2) → A'(-7 ,-2) and B(2 ,3) → B'(-2 ,-3)
Second transformation Under a translation
#((-4),(0))# a point (x ,y) → (x-4 ,y)
hence A'(-7 ,-2) → A''(-11 ,-2) and B'(-2 ,-3) → B''(-6 ,-3)
Third transformation Under a reflection in the y-axis
a point (x ,y) → (-x ,y)
hence A''(-11 ,-2) → A'''(11 ,-2) and B''(-6 ,-3) → B'''(6 ,-3)
Thus after all 3 transformations.
#(7,2)to(11,-2)" and " (2,3)to(6,-3)#
