#A(3,7) and B (3,-4)# . Clockwise rotation of point A is
#alpha=pi/2 :. # Counterclockwise rotation of point A is
#theta=2pi-alpha=2pi-pi/2=(3pi)/2#. New coordinates of
#A(x',y')# can be found by the fomula ,
#x'= xcos theta +ysin theta and y'= y cos theta - x sin theta#
#:.x'= 3*cos((3pi)/2)+7*sin((3pi)/2) = 0+(-7)=-7#
#x'= -7; y'= 7* cos((3pi)/2)- 3 * sin((3pi)/2) #
#= 7 * 0-3 *(-1)=3:. y'=3 :. (x',y') = (-7,3)#
Distance between two points #(x_1,y_1) and (x_2,y_2)# is
#D= sqrt((x_1-x_2)^2+(y_1-y_2)^2)# . Orginal distance between
points #A(3,7) and B (3,-4)# is
#D_o= sqrt((3-3)^2+(7+4)^2)=sqrt 121= 11.0# unit.
New distance between points #A(-7,3) and B (3,-4)# is
#D_n= sqrt((-7-3)^2+(3+4)^2)=sqrt 149~~ 12.2# unit
Distance between A and B changed by #12.2-11.1=1.1# unit .
[Ans]
