Point A is at #(5 ,-8 )# and point B is at #(-3 ,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
Somebody N.
May 27, 2018

See below.

Explanation:

A rotation of #pi/2# clockwise maps:

#(x,y)->(-y,x)#

Points: #A=(5,-8)#, #(-3,3)#

#:.#

#A'=(5,-8)->(-y,x)=(8,5)#

#B'=(-3,3)->(-y,x)=(-3,-3)#

Where #A' and B'# are the images of A and B respectively.

Using the distance formula to find the distance between A and B and A' and B'

#A and B#

#d=sqrt((-3-5)^2+(3-(-8)))=sqrt(185)#

#A' and B'#

#d=sqrt((-3-8)^2+(-3,-5)^2)=sqrt(185)#

We didn't need to even calculate this. A rotation doesn't change the relative distance between points. The question is very ambiguous when it asks for distance between A and B. I have assumed it meant between #A' and B'#.

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