Point A is at $(- 2, 5)$ $(-2 ,5 )$ and point B is at $(2, - 3)$ $(2 ,-3 )$ . Point A is rotated $π$ $pi$ 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 · 2018-03-29T12:20:29

$Decrease in distance due rotation is$ $color(blue)("Decrease in distance due rotation is "$

$color(orange)(vec(AB) - vec(A'B) = 8.94 - 2 = 6.94 " units"$

$A (-2, 5), B (2, -3)$

$vec (AB) = sqrt((-2-2)^2 + (5 + 3)^2) = 8.94 " units"$

$"Point A rotated " pi " clockwise about the origin"$

![https://www.onlinemath4all.com/http://rotation-transformation.html](https://useruploads.socratic.org/xMO9M5zOTQarx2Qu3hx8_rotation%20rules.jpg)

$A (-2,5) -> A'(2, -5)$

$vec (A'B) = sqrt ((2-2)^2 + (-5 +3)^2) = 2 " units"$

$color(blue)("Decrease in distance due rotation is "$

$color(grey)(vec(AB) - vec(A'B) = 8.94 - 2 = 6.94 " units"$

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