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

#(2,3)to(3,6)" and " (3,9)to(-9,5)#

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)#