Point A is at $(-9 ,-6 )$ and point B is at $(-2 ,-7 )$ . 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 · 2018-06-30T02:33:03

$color(brown)(8.23" is the change in the distance between A & B due to the rotation of A by " (3pi)/2 " clockwise about the origin"$

$A (-9,-6), B (-2, -7), " A rotated (3pi)/2 clockwise about origin"$

#"To find change in distance of AB"

Using distance formula between two points,

$bar(AB) = sqrt ((-9 +2)^2 + (-6 +7)^2) = 7.07$

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

$A (-9, -6) to A'(6,-9), " as per rotation rule"$

$bar (A'B) = sqrt((-9-6)^2 + (-6 +9)^2) ~~ 15.3$

$"Change in distance "= 15.3 - 7.07 = 8.23$

$color(brown)(8.23" is the change in the distance between A & B due to the rotation of A by " (3pi)/2 " clockwise about the origin"$

Point A is at (-9 ,-6 )(-9 ,-6 ) and point B is at (-2 ,-7 )(-2 ,-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?