Point A is at $(-5 ,9 )$ and point B is at $(-1 ,4 )$ . 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 · 2018-02-06T12:01:45

New coordinates of $color(brown)(A (-9, -5)$

Increase in distance caused by the rotation is

$color(green)(sqrt145 - sqrt41 ~~ 10.2$ units

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$A (-5,9), B (-1,4)$

Point A is in II quadrant and moves to III quadrant where both x & y are negative.

$vec(AB) = ((-5),(9)) -> vec(A'B) = ((-9),(-5))$

By distance formula,

$vec(AB) = sqrt((-5+1)^2 + (9-4)^2) = sqrt41$

$vec(A'B) = sqrt((-9+1)^2 + (-5-4)^2) = sqrt145$

Increase in distance caused by the rotation is

$color(green)(sqrt145 - sqrt41 ~~ 10.2$ units

Point A is at (-5 ,9 )(-5 ,9 ) and point B is at (-1 ,4 )(-1 ,4 ). 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?