Point A is at $(2 ,-6 )$ and point B is at $(-8 ,-3 )$ . 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 · 2018-02-06T10:21:08

New coordinate of $color(red)(A (-5, -2)$

Distance changed (increase) between A & B by $(pi/2)$ clockwise rotation of A about the origin is $color(green)(sqrt109 - sqrt10 ~~ 7.28)$

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A (2, -6), B(-8, -3)

Point A rotated clockwise about the origin by $pi/2$

That means A changes from fourth quadrant to third quadrant.

Both x & y are negative.That means, x -> -y and y -> x.

$A ((2),(-5)) -> A'((-5),(-2))$

$AB = sqrt((2-(-8))^2 + (-6 - (-3))^2) = sqrt109$

$A'B = sqrt((-5-(-8))^2 + (-2 - (-3))^2) = sqrt10$

Distance changed between A & B by th#pi/2) clockwise rotation of A about the origin is

$A'B - AB = color(green)(sqrt109 - sqrt10 ~~ 7.28)$

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