Point A is at #(8 ,-4 )# and point B is at #(2 ,6 )#. 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 · 2018-02-06T11:35:27

New coordinate of #color(red)(A (4,8)#

Distance change (reduction) between A & B by rotating A around origin by

#(3pi)/2# clockwise -s #color(green)(sqrt136 - sqrt8 ~~ 8.83# units

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#A (8, -4), B (2,6)

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

A moves to A' from IV quadrant to I quadrant.

#A(8, -4) -> A'(4,8)#

Using distance formula,

#vec(AB) = sqrt((8-2)^2 + (-4-6)^2) = sqrt136#

#vec(A'B) = sqrt((4-2)^2 + (8-6)^2) = sqrt8#

Distance change (reduction) between A & B by rotating A around origin by

#(3pi)/2# clockwise -s #color(green)(sqrt136 - sqrt8 ~~ 8.83# units