Point A is at #(2 ,9 )# and point B is at #(-8 ,-3 )#. Point A is rotated #pi/2 # 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?

1 Answer
Narad T.
Jul 8, 2017

The new coordinates are #=(9,-2)# and the distance has changed by #=1.41#

Explanation:

The rotation of #pi/2# clockwise about the origin transforms the point #A# into #A'#

The coordinates of #A'# are

#((0,1),(-1,0))*((2),(9))=((9),(-2))#

Distance #AB# is

#=sqrt((-8-2)^2+(-3-9)^2)#

#=sqrt(244)#

Distance #A'B# is

#=sqrt((-8-9)^2+(-3+2)^2)#

#=sqrt290#

The distance has changed by

#=sqrt290-sqrt244#

#=1.41#

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