# Point A is at #(1 ,-9 )# and point B is at #(-2 ,8 )#. 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?

The new point A will be at

Difference in distance

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The new coordinates of point A after rotating (3π)/2 clockwise about the origin are (-9, -1). The distance between the original point A and point B is sqrt(170). After the rotation, the distance between the new point A and point B is also sqrt(170). Therefore, the distance between points A and B has not changed after the rotation.

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