Point A is at $(-2 ,5 )$ and point B is at $(-3 ,3 )$ . 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 · 2018-07-15T09:49:47

As below.

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

#"To find change in distance of AB"

Using distance formula between two points,

$bar(AB) = sqrt ((-2+ 3)^2 + (5 - 3)^2) ~~ 2.2361$

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

$A (-2, 5) to A'(2, -5), " as per rotation rule"$

$bar (A'B) = sqrt((2 + 3)^2 + (-5 - 3)^2) = 9.434$

$"Change in distance "= 9.434 - 2.2361 = 7.198$

$color(blue)(7.198 " is the change in the distance between A & B"$ $color(crimson)("due to the rotation of A by " pi " clockwise about the origin"$

Point A is at (-2 ,5 )(-2 ,5 ) and point B is at (-3 ,3 )(-3 ,3 ). 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?