Point A is at $(8 ,-4 )$ and point B is at $(2 ,6 )$ . 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 · 2018-02-06T11:35:27

New coordinate of $color(red)(A (4,8)$

Distance change (reduction) between A & B by rotating A around origin by

$(3pi)/2$ clockwise -s $color(green)(sqrt136 - sqrt8 ~~ 8.83$ units

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#A (8, -4), B (2,6)

Point A rotated clockwise about the origin by $(3pi)/2$

A moves to A' from IV quadrant to I quadrant.

$A(8, -4) -> A'(4,8)$

Using distance formula,

$vec(AB) = sqrt((8-2)^2 + (-4-6)^2) = sqrt136$

$vec(A'B) = sqrt((4-2)^2 + (8-6)^2) = sqrt8$

Distance change (reduction) between A & B by rotating A around origin by

$(3pi)/2$ clockwise -s $color(green)(sqrt136 - sqrt8 ~~ 8.83$ units

Point A is at (8 ,-4 )(8 ,-4 ) and point B is at (2 ,6 )(2 ,6 ). 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?