Point A is at $(5 ,7 )$ and point B is at $(-6 ,-3 )$ . 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 · 2018-04-08T05:20:25

$color(brown)("There is no change in the distance between A & B due to the rotation of " (3pi)/2 " clockwise about the origin"$

$A (5,7), B (-6, -3), " A rotated (3pi)/2 clockwise about origin"$

#"To find change in distance of AB"

Using distance formula between two points,

$bar(AB) = sqrt ((5 + 6)^2 + (7 + 3)^2) = 14.87$

![https://www.onlinemath4all.com/http://rotation-transformation.html](https://useruploads.socratic.org/VA3bKvvS3K8G1tSlViNi_rotation%20rules.jpg)

$A (5, 7) to A'(-7,5), " as per rotation rule"$

$B(-6, -3) to B'(3, -6), " as per rotation rule"$

$bar (A'B') = sqrt((-7-3)^2 + (5 + 6)^2) = 14.87$

$color(brown)("There is no change in the distance between A & B due to the rotation of " (3pi)/2 " clockwise about the origin"$

Point A is at (5 ,7 )(5 ,7 ) and point B is at (-6 ,-3 )(-6 ,-3 ). 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?