Point A is at #(4 ,-8 )# and point B is at #(-1 ,-2 )#. 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 · 2018-03-20T10:54:32

Increase in distance due to rotation of point A (4,-8) about origin by #(3pi)/2# clockwise is

#color(indigo)(vec(A'B) - vec (AB) = sqrt117 - sqrt61 = 3#

#"Point " A (4,-8), "Point "B(-1,-2)#

Point A rotated about origin by #(3pi)/2# clockwise.

Using distance frmula,

#vec(AB) = sqrt((4+1)^2 + (-8+2)^2) = sqrt61#

#A (4, -8) - > A'(8,4), " (from quadrant IV to quadrant I)"#

#vec(A'B) = sqrt((8+1)^2 + (4 + 2)^2) = sqrt117#

Increase in distance due to rotation of point A (4,-8) about origin by #(3pi)/2# clockwise is

#color(indigo)(vec(A'B) - vec (AB) = sqrt117 - sqrt61 = 3#