Point A is at #(9 ,5 )# and point B is at #(2 ,4 )#. Point A is rotated #pi # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

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Answer 1 · 2017-07-06T09:28:32

The new coordinates are #(-9,-5)# and the distance has changed by #=7.14#

The matrix of a rotation clockwise by #pi# about the origin is

#((-1,0),(0,-1))#

Therefore, the transformation of point #A# is

#A'=((-1,0),(0,-1))((9),(5))=((-9),(-5))#

The distance #AB# is

#AB=sqrt((2-9)^2+(4-5)^2)#

#=sqrt(49+1)#

#=sqrt50#

The distance #A'B# is

#A'B=sqrt((2-(-9))^2+(4-(-5))^2)#

#=sqrt(121+81)#

#=sqrt202#

The distance has changed by

#=sqrt202-sqrt50#

#=7.14#