A line segment has endpoints at #(4 ,1 )# and #(5 ,6)#. If the line segment is rotated about the origin by #pi #, translated vertically by #-2 #, and reflected about the x-axis, what will the line segment's new endpoints be?
1 Answer
Jun 11, 2016
(4 ,1) → (-4 ,3) , (5 ,6) → (-5 ,8)
Explanation:
Since there are 3 transformations I am naming the endpoints A(4 ,1) and B(5 ,6) so that we can follow what happens to them after each transformation.
First transformation: Under a rotation about the origin of
#pi# a point (x ,y) → (-x ,-y)
hence A(4 ,1) → A'(-4 ,-1) and B(5 ,6) → B'(-5 ,-6)
Second transformation: Under a translation of
#((0),(-2))# a point (x ,y) → (x ,y-2)
hence A'(-4 ,-1) → A'' (-4 ,-3) and B'(-5 ,-6) → B''(-5 ,-8)
Third transformation: Under a reflection in the x-axis
a point (x ,y) → (x ,-y)
hence A''(-4 ,-3) → A'''(-4 ,3) and B''(-5 ,-8) → B'''(-5 ,8)
Thus (4 ,1) → (-4 ,3) and (5 ,6) → (-5 ,8)
