Point A is at $(-8 ,2 )$ and point B is at $(7 ,-1 )$ . 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 · 2018-02-22T09:48:06

Decrease in distance due to the rotation by $pi$ , $d =color(green)( 4.9985$

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$A (-8,2), B (7,-1)$

Rotated about the origin by $pi/2$ , clockwise.

$vec(AB:) = sqrt((-8-7)^2 + (2+1)^2) = 15.2971$

$A ((-8),(2)) - > A’((2),(8))$

$vec(A’B) = sqrt((2-7)^2 + (8+1)^2) = 10.2956$

Decrease in distance due to the rotation by $pi$

$d = 15.2971 - 10.2956 = 4.9985$

Point A is at (-8 ,2 )(-8 ,2 ) and point B is at (7 ,-1 )(7 ,-1 ). 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?