Point A is at $(-3 ,-4 )$ and point B is at $(-5 ,-8 )$ . 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?

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Answer 1 · 2018-06-30T02:45:48

$color(cyan)(5.83 " is the change in the distance between A & B"$ $color(cyan)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"$

$A (-3, -4), B (-5, -8), " A rotated "(3pi)/2 " clockwise about origin"$

#"To find change in distance of AB"

Using distance formula between two points,

$bar(AB) = sqrt ((-3 + 5)^2 + (-4 + 8)^2) ~~ 4.47$

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

$A (-3, -4) to A'(4, -3), " as per rotation rule"$

$bar (A'B) = sqrt((4 + 5)^2 + (-3 + 8)^2) ~~ 10.3$

$"Change in distance "= 10.3 - 4.47 = 5.83$

$color(cyan)(5.83 " is the change in the distance between A & B"$ $color(cyan)("due to the rotation of A by " (3pi)/2 " clockwise about the origin"$

Point A is at (-3 ,-4 )(-3 ,-4 ) and point B is at (-5 ,-8 )(-5 ,-8 ). 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?