Point A is at $(-7 ,7 )$ and point B is at $(5 ,1 )$ . 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 · 2018-02-07T01:58:15

New coordinates of A are $color(red)(7, -7)$

Change ( reduction ) in length of $vec(AB)$ due to the rotation :

$color(green)(vec(AB) - vec(A'B) = 13.42 - 8.25 = 5.17)$

Given : A (-7, 7), B (5, 1). Rotated clockwise by $pi$ about the origin.

Point A is in II quadrant and roated to IV quadrant

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$A((-7),(7)) -> A'((7),(-7))$

New coordinates of A are $color(red)(7, -7)$

$vec(AB) = sqrt((-7-5)^2 + (7-1)^2) ~~ color(blue)(13.42)$

$vec(A'B) = sqrt((7-5)^2 + (-7-1)^2) ~~ color(blue)(8.25)$

Change (reduction) in length of $vec(AB)$ due to the rotation :

$color(green)(vec(AB) - vec(A'B) = 13.42 - 8.25 = 5.17)$

Point A is at (-7 ,7 )(-7 ,7 ) and point B is at (5 ,1 )(5 ,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?