Point A is at $(6 ,-8 )$ and point B is at $(-3 ,8 )$ . 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 · 2018-02-22T14:07:08

Decrease in distance due to rotation of coordinates of A

$vec(AB) - vec(A’B) = color(red)(3.4915$

$vec (AB) = sqrt ((6+3)^2 + (-8-8)^2) = 18.3576$

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$A((6),(-8)) -> A’ ((-8),(-6))$

$vec(A’B) = sqrt((-8+3)^2 + (-6-8)^2) = 14.8661$

Decrease in distance due to rotation of coordinates of A

$vec(AB) - vec(A’B) = 18.3576 - 14.8661 = color(red)(3.4915$

Point A is at (6 ,-8 )(6 ,-8 ) and point B is at (-3 ,8 )(-3 ,8 ). Point A is rotated pi/2 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?