Point A is at $(-7 ,-1 )$ and point B is at $(2 ,-4 )$ . Point A is rotated $pi$ 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 · 2018-06-30T02:38:22

$color(indigo)(2.42" is the change in the distance between A & B due to the rotation of A by " (3pi)/2 " clockwise about the origin"$

$A (-7, -1), B (2, -4), " A rotated " pi " clockwise about origin"$

#"To find change in distance of AB"

Using distance formula between two points,

$bar(AB) = sqrt ((-7 -2)^2 + (-1 +4)^2) ~~ 9.49$

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

$A (-7, -1) to A'(7,1), " as per rotation rule"$

$bar (A'B) = sqrt((7-2)^2 + (1+4)^2) ~~ 7.07$

$"Change in distance "= 9.49 - 7.07 = 2.42$

$color(indigo)(2.42" is the change in the distance between A & B due to the rotation of A by " (3pi)/2 " clockwise about the origin"$

Point A is at (-7 ,-1 )(-7 ,-1 ) and point B is at (2 ,-4 )(2 ,-4 ). Point A is rotated pi pi 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?