Point A is at $(1 ,-1 )$ and point B is at $(-2 ,1 )$ . 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 · 2018-02-07T02:47:13

New coordinates of $color(red)(A ((1),(1))$

Change (reduction) in distance from $bar(AB), bar(A'B)$ is

$=> sqrt13 - 3 ~~ color(green)(0.61)$

A (1, -1), B (-2,1) and rotated by $(3pi)/2$ clockwise about the origin.

Point A moves from IV quadrant to I quadrant.

$A((1),(-1)) ->A'((1),(1))$

Distance $vec(AB) = sqrt((1+2)^2 + (-1-1)^2) = color(blue)(sqrt13$

Distance $vec(A'B) = sqrt((1+2)^2 + (1-1)^2) = color(blue)3$

Change (reduction) in distance from $bar(AB), bar(A'B)$ is

$=> sqrt13 - 3 ~~ color(green)(0.61)$

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