A line segment has endpoints at #(4 ,9 )# and #(2 ,9 )#. If the line segment is rotated about the origin by #( pi)/2 #, translated vertically by #-8 #, and reflected about the x-axis, what will the line segment's new endpoints be?
1 Answer
Jun 8, 2016
(4 ,9) → (-9 ,4) and (2 ,9) → (-9 ,6)
Explanation:
Since there are 3 transformations being performed here I will name the endpoints A (4 ,9) and B (2 ,9) so that we can follow what happens to them after each transformation.
First transformation : Rotation about the origin of
#pi/2# a point (x ,y) → (-y ,x)
hence A(4 ,9) → A'(-9 ,4) and B(2 ,9) → B'(-9 ,2)
Second transformation : Under a translation
#((0),(-8))# a point (x ,y) → (x ,y-8)
hence A'(-9 ,4) → A'' (-9 ,-4) and B'(-9 ,2) → B''(-9 ,-6)
Third transformation : Under a reflection in x-axis
a point (x ,y) → (x ,-y)
hence A''(-9 ,-4) → A'''(-9 ,4) and B''(-9 ,-6) → B'''(-9 ,6)
Thus (4 ,9) → (-9 ,4) and (2 ,9) → (-9 ,6)
