Point A is at #(5 ,1 )# and point B is at #(2 ,-4 )#. 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 · 2016-11-24T12:52:08

#"The new coordinates of A is (-1,5)"#

#"distance :"sqrt(90)#

#"draw A(5,1) and B(2,-4)"#

enter image source here

#(2pi)-(3pi)/2=pi/2#

#"clockwise "(3pi)/2 " equals counterclockwise "pi/2 #

#"so " A(x,y) " "A'(-y,x)#

#"The new Position of A is "A'(-1,5)#

enter image source here

#"distance between B and A' can be calculated using the triangle A'DB"#

#A'B=sqrt(3^2+9^2)#

#A'B=sqrt(9+81)#

#A'B=sqrt(90)#