Point A is at #(-9 ,-4 )# and point B is at #(-5 ,-8 )#. 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?

Question

1004 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-05T03:58:41

The new Point #A(4, -9)#
Difference #=d_n-d_o=sqrt82-4sqrt2=5.65685#

Original distance between point A and B
#d_o=sqrt((x_a-x_b)^2+(y_a-y_b)^2)#
#d_o=sqrt((-9--5)^2+(-4--8)^2)#
#d_o=sqrt((-4)^2+(4)^2)#
#d_o=4sqrt2#

the new distance #d_n#

Let #A(x_a, y_a)=(4, -9)#
#d_n=sqrt((x_a-x_b)^2+(y_a-y_b)^2)#

#d_n=sqrt((4--5)^2+(-9--8)^2)#
#d_n=sqrt((9)^2+(-1)^2)#
#d_n=sqrt(82)#

Difference #=d_n-d_o=sqrt82-4sqrt2=5.65685#

God bless....I hope the explanation is useful.