A line segment has endpoints at #(2 ,3 )# and #(3 ,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
Dec 1, 2016
Explanation:
Since there are 3 transformations to be performed here, label the endpoints A (2 ,3) and B (3 ,9)
First Transformation Under a rotation about the origin of
#pi/2#
#" a point " (x,y)to(-y,x)# Hence A(2 ,3) → A'(-3 ,2) and B(3 ,9) → B' (-9 ,3)
Second Transformation Under a translation
#((0),(-8))#
#" a point " (x,y)to(x,y-8)# Hence A'(-3 ,2) → A''(3 ,-6) and B'(-9 ,3) → B''(-9 ,-5)
Third transformation Under a reflection in the x-axis
#" a point " (x,y)to(x,-y)# Hence A''(3 ,-6) → A'''(3 ,6) and B''(-9 ,-5) → B'''(-9 ,5)
Thus after all 3 transformations.
#(2,3)to(3,6)" and " (3,9)to(-9,5)#
