Point A is at #(-1 ,4 )# and point B is at #(-3 ,7 )#. Point A is rotated #(3pi)/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?

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Answer 1 · 2016-03-14T10:54:55

Distance has increased by #4.456#

A point #(x,y)# rotated clockwise #3pi/2# means rotated anticlockwise #pi/2# and hence new coordinates are #(-y,x)#.

Hence the coordinates of point #A# #(-1,4)# will become #(-4,-1)#.

The distance between point #A# #(-1,4)# and point #B# #(-3,7)# is

#sqrt(((-3)-(-1))^2+(7-4)^2)=sqrt((-2)^2+3^2)#

= #sqrt(4+9)=sqrt13=3.606#

The distance between rotated point #A# #(-4,-1)# and point #B# #(-3,7)# is

#sqrt(((-3)-(-4))^2+(7-(-1))^2)=sqrt(1^2+8^2)#

= #sqrt(1+64)=sqrt65=8.062#

Hence, distance has increased by #8.062-3.606=4.456#