Point A is at #(-2 ,6 )# and point B is at #(-7 ,-5 )#. 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 #=(6,2)# and the distance has changed by #=2.68#

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),(6))=((6),(2))#

Distance #AB# is

#=sqrt((-7+2)^2+(-5-6)^2)#

#=sqrt(25+121)#

#=sqrt(146)#

Distance #A'B# is

#=sqrt((-7-6)^2+(-5-2)^2)#

#=sqrt(169+49)#

#=sqrt(218)#

The distance has changed by

#=sqrt218-sqrt146#

#=2.68#

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