Point A is at $(-7 ,4 )$ and point B is at $(2 ,-1 )$ . 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 · 2018-02-22T06:50:05

Due to rotation of A distance reduced between A and B by 4.4646

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$A((-7),(4)) -> A’((7),(-4))$

$vec (AB) = sqrt((-7-2)^2 + (4+1)^2) = 10.2956$

$vec (A’B) = sqrt((7-2)^2 + (-4+1)^2) = 5.831$

Distance change

$vec(AB) - vec (A’B) = 10.2956 - 5.831 = 4.4646$

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