Point A is at $(2 ,5 )$ and point B is at $(1 ,-6 )$ . 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 · 2018-02-22T08:04:52

$vec(AB)$ has reduced by $color(brown)(7.8831)$ due to rotation of $pi$ clockwise about the origin.

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$A((2),(5)) -> A’((-2),(-5))$ . I to III quadrant.

$vec (AB) = sqrt ((2-1)^2 + (5+6)^2) = 11.0454$

$vec (A’B) = sqrt ((-2-1)^2 + (-5+6)^2) = 3.1623$

$vec(AB) - vec(A’B) = 11.0454 - 3.1623 = 7.8831$

Point A is at (2 ,5 )(2 ,5 ) and point B is at (1 ,-6 )(1 ,-6 ). 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?