Point A is at $(1 ,3 )$ and point B is at $(-1 ,2 )$ . 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 · 2018-03-20T10:17:18

Increase in distance due to rotation of coordinates of A about origin by $pi/2$ clockwise is

$vec(AB) - vec(A’B) = color(red)(2.7639$

$vec (AB) = sqrt ((1+1)^2 + (3-2)^2) = sqrt5$

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$A((1),(3)) -> A’ ((3),(-1))$

$vec(A’B) = sqrt((3+1)^2 + (-1-2)^2) = sqrt25 = 5$

Increase in distance due to rotation of coordinates of A

$vec(A'B) - vec(AB) = 5- sqrt5 = color(red)(2.7639$

Point A is at (1 ,3 )(1 ,3 ) and point B is at (-1 ,2 )(-1 ,2 ). 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?