Point A is at $(-8 ,-2 )$ and point B is at $(7 ,-3 )$ . 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 · 2018-02-14T07:12:16

Decrease in distance by rotating A to A’ is

$sqrt226 - sqrt202 ~~ color(purple)(0.82)$

$A ((-8),(-2)), B ((7),(-3))$

Point A rotated clockwise by $pi/2$ about the origin.

Let A’ be the new point of A after rotation.

$A’((-2),(8))$ . From third quadrant to second quadrant.

$vec(AB) = sqrt((-8-7)^2 + (-2+3)^2) = sqrt226$

$vec (A’B) = sqrt((-2-7)^2 + (8+3)^2) = sqrt202$

Decrease in distance by rotating A to A’ is

$sqrt226 - sqrt202 ~~ color(purple)(0.82)$

Point A is at (-8 ,-2 )(-8 ,-2 ) and point B is at (7 ,-3 )(7 ,-3 ). 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?