Point A is at $(-5 ,9 )$ and point B is at $(-3 ,4 )$ . 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 · 2018-03-29T08:06:21

$color(indigo)("Increase in distance due to the rotation of A is "$

$color(purple)(= vec(A'B) - vec(AB) = 6.08 - 5.39 = 0.69 " units"$

$A(-5,9), B (-3,4)$

$vec(AB) = sqrt((-5+3)^2 + (9-4)^2) = 5.39 " units"$

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

![https://www.onlinemath4all.com/http://rotation-transformation.html](https://useruploads.socratic.org/bZDPsMSfSx29x75Lcx0p_rotation%20rules.jpg)

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

$vec(A'B) sqrt((-9+3)^2 + (5-4)^2) = 6.08 " units$

$color(indigo)("Increase in distance due to the rotation of A is "$

$color(purple)(= vec(A'B) - vec(AB) = 6.08 - 5.39 = 0.69 " units"$

Point A is at (-5 ,9 )(-5 ,9 ) and point B is at (-3 ,4 )(-3 ,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?