Point A is at $(4 ,-5 )$ and point B is at $(-6 ,-2 )$ . 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 · 2018-02-16T15:09:52

New coordinates $A’ (-5,-4)$

Change in distance $1.3849$ , reduction.

Given $A (4, -5), B (-6,-2). Rotated about origin by$ (3pi)/2#

To find A’ and $A’B - AB$

$vec(AB) = sqrt((4+6)^2 + (-5+2)^2) = sqrt109$

Coordinates of A’ (-5,-4)

$vec(A’B) = sqrt((-5-4)^2 + (-4+5)^2) = sqrt 82$

Change in distance $vec(AB) - vec(A’B) = sqrt109 - sqrt82 ~~ 1.3849$

Point A is at (4 ,-5 )(4 ,-5 ) and point B is at (-6 ,-2 )(-6 ,-2 ). Point A is rotated (3pi)/2 (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?