A line segment has endpoints at #(5 ,3 )# and #(5 ,4)#. If the line segment is rotated about the origin by #pi /2 #, translated horizontally by #-1 #, and reflected about the x-axis, what will the line segment's new endpoints be?
1 Answer
Oct 2, 2016
Explanation:
Since there are 3 transformations to be performed, name the endpoints A(5 ,3) and B(5 ,4) so that we can follow the changes that occur to them.
First transformation Under a rotation about the origin of
#pi/2# a point (x , y) → (-y ,x)
hence A(5 ,3) → A'(-3 ,5) and B(5 ,4) → B'(-4 ,5)
Second transformation Under a translation
#((-1),(0))# a point (x ,y) → (x-1 ,y+0) → (x-1 ,y)
hence A'(-3 ,5) → A''(-4 ,5) and B'(-4 ,5) → B''(-5 ,5)
Third transformation Under a reflection in the x-axis
a point (x ,y) → (x ,-y)
hence A''(-4 ,5) → A'''(-4 ,-5) and B''(-5 ,5) → B'''(-5 ,-5)
Thus after all 3 transformations.
#(5,3)to(-4,-5)" and " (5,4)to(-5,-5)#
