Point A is at #(-2 ,5 )# and point B is at #(-3 ,8 )#. Point A is rotated #pi # 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 · 2017-06-07T12:14:56

The new point is #=(2,-5)# and the distance has changed by #=12.93#

The matrix of a rotation clockwise by #pi# about the origin is

#=((cos(-pi),-sin(-pi)),(sin(-pi),cos(-pi)))=((-1,0),(0,-1))#

Therefore, the trasformation of point #A# into #A'# is

#A'=((-1,0),(0,-1))((-2),(5))=((2),(-5))#

Distance #AB# is

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

#=sqrt(1+9)#

#=sqrt10#

Distance #A'B# is

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

#=sqrt(25+169)#

#=sqrt194#

The distance has changed by

#=sqrt194-sqrt10#

#=12.93#