Point A is at $(5 ,2 )$ and point B is at $(2 ,-4 )$ . 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 · 2018-02-06T11:46:23

New coordinate of $color(red)(A (-2,5)$

Reduction in distance due to rotation around origin is

$color(green)(bar(AB) - bar(A'B) = sqrt45 - sqrt17 ~~ 2.59)$ units

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Point A (5,2), Point B (2, -4)

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

Point A moves from Quadrant I to Quadrant II

$A ((5),(2)) -> A'( (-2),( 5))$

Distance formula $d = sqrt((x_2-x_1)^2 + (y_2 - y_1)^2)$ ,

$bar(AB) = sqrt((5-2)^2 + (2-(-4))^2) = sqrt45$

$bar(A'B) = sqrt((-2-2)^2 + (5-(-4))^2) = sqrt17$

Reduction in distance due to rotation around origin is

$color(green)(bar(AB) - bar(A'B) = sqrt45 - sqrt17 ~~ 2.59)$ units

Point A is at (5 ,2 )(5 ,2 ) and point B is at (2 ,-4 )(2 ,-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?