Point A is at $(-2 ,9 )$ and point B is at $(-1 ,4 )$ . Point A is rotated $(3pi)/2$ 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 · 2018-02-07T03:29:54

New coordinates of $color(red)(A' ((-9),(-2))$

Change in distance between A & B is $color(blue)(+4.9)$

Point A (-2,9), B (-1,4). Point A Rotated about origin by $(3pi)/2$ clockwise.

That means A moves from II quadrant to III quadrant.

Distance $vec(AB) = sqrt((-2+1)^2 + (9-4)^2) = sqrt26 ~~ color(red)(5.1)$

$A ((-2),(9)) to A' ((-9),(-2))$

Distance $vec(A'B) = sqrt((-9+1)^2 + (-2-4)^2) = color(red)(10$

Change in distance $=color(blue)(10 - 5.1 = +4.9)$

Point A is at (-2 ,9 )(-2 ,9 ) and point B is at (-1 ,4 )(-1 ,4 ). Point A is rotated (3pi)/2 (3pi)/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?