Point A is at $(-5 ,9 )$ and point B is at $(-6 ,7 )$ . 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 · 2018-03-20T10:35:56

Increase in distance due to rotaion of point A about origin by $(3pi)/2$ clockwise is

$color(brown)(vec(A'B) - vec(AB) = sqrt153 - sqrt5 = 10.13$ units

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$"Point" A (-5,9), B (-6,7)$

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

Point A moves from II to III quadrant.

$A (-5,9) -> A'(-9,-5)$

Using distance formula,

$vec(AB) = sqrt((-5 +6)^2 + (9-7)^2) = sqrt5$

$vec(A'B) = sqrt((-9+6)^2 + (-5-7)^2) = sqrt153$

Increase in distance due to rotaion of point A about origin by $(3pi)/2$ clockwise is

$vec(A'B) - vec(AB) = sqrt153 - sqrt5 = 10.13$

Point A is at (-5 ,9 )(-5 ,9 ) and point B is at (-6 ,7 )(-6 ,7 ). 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?