Point A is at #(-1 ,-4 )# and point B is at #(-3 ,-1 )#. Point A is rotated #pi/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 · 2018-03-20T11:16:03

Decrease in distance due to the rotation of A about origin by #(pi/2)# clockwise is

#color(red)(vec(AB) - vec(A'B) = sqrt13 - sqrt5 = 1.3695#

#"Point " A(-1, -4), "Point " B (-3, 1)#

Point A rotated about origin by #pi/2# clockwise.

#A (-1, -4) -> A' (-4, 1), " from III to II quadrant"#

Using distance formula between two points,

#vec(AB) = sqrt((-1+3)^2 + (-4 + 1)^2 ) = sqrt13#

#vec (A'B) = sqrt((-4+3)^2 + (1 + 1)^2) = sqrt5#

Decrease in distance due to the rotation of A about origin by #(pi/2)# clockwise is

#color(red)(vec(AB) - vec(A'B) = sqrt13 - sqrt5 = 1.3695#