Point A is at #(-8 ,-2 )# and point B is at #(2 ,-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 14, 2017

The new coordinates are #=(-2,8)# and the distance has changed by #=1.65#

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))*((-8),(-2))=((-2),(8))#

Distance #AB# is

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

#=sqrt(100+1)#

#=sqrt(101)#

Distance #A'B# is

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

#=sqrt(16+121)#

#=sqrt(137)#

The distance has changed by

#=sqrt137-sqrt101#

#=1.65#

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