Point A is at $(-1 ,-5 )$ and point B is at $(-2 ,4 )$ . Point A is rotated $pi/2$ 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 · 2018-03-29T08:13:42

$color(red)("Decrease in distance due to the rotation is "$

$color(crimson)(= vec(AB) - vec(A'B) = 9.055 - 4.243 = 4.812 " units"$

$A (-1, -5), B (-2, 4)$

$"Point A rotated " pi/2 " clockwise about the origin"$

$vec(AB) = sqrt((-1+2)^2 + (-5-4)^2) = 9.055 " units"$

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

$A (-1, -5) rarr A' (-5, 1)$

$vec (A'B) = sqrt((-5 + 2)^2 + (1 - 4)^2) = 4.243 " units"$

$color(red)("Decrease in distance due to the rotation is "$

$color(crimson)(= vec(AB) - vec(A'B) = 9.055 - 4.243 = 4.812 " units"$

Point A is at (-1 ,-5 )(-1 ,-5 ) and point B is at (-2 ,4 )(-2 ,4 ). Point A is rotated pi/2 pi/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?