A line segment has endpoints at #(9 ,6 )# and #(5 ,3)#. If the line segment is rotated about the origin by #pi /2 #, translated vertically by #2 #, and reflected about the x-axis, what will the line segment's new endpoints be?
1 Answer
Nov 10, 2016
Explanation:
Since there are 3 transformations to be performed here, label the points A(9 ,6) and B(5 ,3) so that the change to each point after each transformation can be noted.
First transformation Under a rotation about the origin if
#pi/2#
#" a point" (x,y)to(y,-x)# hence A(9 ,6) →A'(6 ,-9) and B(5 ,3) → B'(3 ,-5)
Second transformation Under a translation
#((0),(2))#
#" a point" (x,y)to(x+0,y+2)# hence A'(6 ,-9) → A''(6 ,-7) and B'(3 ,-5) → B''(3 ,-3)
Third transformation Under a reflection in the x-axis
#" a point" (x,y)to(x,-y)# hence A''(6 ,-7) → A'''(6 ,7) and B''(3 ,-3) → B'''(3 ,3)
After all 3 transformations.
#(9,6)to(6,7)" and " (5,3)to(3,3)#
