Point A is at $(4 ,2 )$ and point B is at $(3 ,6 )$ . 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 · 2018-02-15T10:00:35

Increase in distance due to the rotation of point A by $pi/2$ around origin is $color(red)(= 5.9267$

$A ((4),(2)), B ((3),(6))$ . A rotated around origin by $pi/2$

Using distance formula $vec(AB) = sqrt((4-3)^2 + (2-6)^2) ~~ 4.1231$

$A’ => ((2),(-4))$ from first to fourth quadrant.

$vec(A’B) = sqrt((3-2)^2 + (-4-6)^2) ~~10.0498$

Increase in distance due to the rotation of point A by $pi/2$ around origin is $color(red)(10.0498-4.1231 = 5.9267$

Point A is at (4 ,2 )(4 ,2 ) and point B is at (3 ,6 )(3 ,6 ). 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?